DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP086^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n017.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 08:55:26 AM UTC 2026

% Result   : Theorem 34.97s 6.49s
% Output   : Refutation 34.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP086^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34  % Computer : n017.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Feb 24 08:24:26 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.47  ---- Original DTF file ---
% 0.19/0.47  thf(spec,logic,$$dhol).
% 0.19/0.47  %------------------------------------------------------------------------------
% 0.19/0.47  % File     : ITP086^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.47  % Domain   : Interactive Theorem Proving
% 0.19/0.47  % Problem  : Sledgehammer KnowledgeKeysSecrets problem prob_194__3293238_1
% 0.19/0.47  % Version  : Especial.
% 0.19/0.47  % English  :
% 0.19/0.47  
% 0.19/0.47  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.47  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.47  % Source   : [Des21]
% 0.19/0.47  % Names    : KnowledgeKeysSecrets/prob_194__3293238_1 [Des21]
% 0.19/0.47  
% 0.19/0.47  % Status   : Theorem
% 0.19/0.47  % Rating   : 0.33 v8.2.0, 0.00 v7.5.0
% 0.19/0.47  % Syntax   : Number of formulae    :  359 ( 119 unt;  56 typ;   0 def)
% 0.19/0.47  %            Number of atoms       :  986 ( 269 equ;   0 cnn)
% 0.19/0.47  %            Maximal formula atoms :   13 (   3 avg)
% 0.19/0.47  %            Number of connectives : 3969 ( 107   ~;  28   |;  89   &;3297   @)
% 0.19/0.47  %                                         (   0 <=>; 448  =>;   0  <=;   0 <~>)
% 0.19/0.47  %            Maximal formula depth :   20 (   8 avg)
% 0.19/0.47  %            Number of types       :    5 (   4 usr)
% 0.19/0.47  %            Number of type conns  :  128 ( 128   >;   0   *;   0   +;   0  <<)
% 0.19/0.47  %            Number of symbols     :   53 (  52 usr;   5 con; 0-3 aty)
% 0.19/0.47  %            Number of variables   : 1029 (  76   ^; 904   !;  23   ?;1029   :)
% 0.19/0.47  %                                         (  26  !>;   0  ?*;   0  @-;   0  @+)
% 0.19/0.47  % SPC      : TH1_THM_EQU_NAR
% 0.19/0.47  
% 0.19/0.47  % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:14.132
% 0.19/0.47  %------------------------------------------------------------------------------
% 0.19/0.47  % Could-be-implicit typings (5)
% 0.19/0.47  thf(ty_t_Secrecy__types_OExpression,type,
% 0.19/0.47      secrecy_Expression: $tType ).
% 0.19/0.47  
% 0.19/0.47  thf(ty_t_Secrecy__types_OspecID,type,
% 0.19/0.47      secrecy_specID: $tType ).
% 0.19/0.47  
% 0.19/0.47  thf(ty_t_Secrecy__types_OchanID,type,
% 0.19/0.47      secrecy_chanID: $tType ).
% 0.19/0.47  
% 0.19/0.47  thf(ty_t_Set_Oset,type,
% 0.19/0.47      set: $tType > $tType ).
% 0.19/0.47  
% 0.19/0.47  thf(ty_t_Nat_Onat,type,
% 0.19/0.47      nat: $tType ).
% 0.19/0.47  
% 0.19/0.47  % Explicit typings (51)
% 0.19/0.47  thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.19/0.47      bounded_lattice: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_HOL_Otype,type,
% 0.19/0.47      type: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Obot,type,
% 0.19/0.47      bot: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Oord,type,
% 0.19/0.47      ord: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.47      order: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Olattice,type,
% 0.19/0.47      lattice: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.47      linorder: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.47      preorder: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Orderings_Oorder__bot,type,
% 0.19/0.47      order_bot: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.19/0.47      boolean_algebra: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.19/0.47      semilattice_inf: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.19/0.47      semilattice_sup: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.19/0.47      bounded_lattice_bot: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.19/0.47      bounde1808546759up_bot: 
% 0.19/0.47        !>[A: $tType] : $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.19/0.47      uminus_uminus: 
% 0.19/0.47        !>[A: $tType] : ( A > A ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.19/0.47      inf_inf: 
% 0.19/0.47        !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.19/0.47      sup_sup: 
% 0.19/0.47        !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.19/0.47      bot_bot: 
% 0.19/0.47        !>[A: $tType] : A ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.47      ord_less_eq: 
% 0.19/0.47        !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oeout,type,
% 0.19/0.47      eout: secrecy_specID > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_OeoutM,type,
% 0.19/0.47      eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_OexprChannel,type,
% 0.19/0.47      exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oine,type,
% 0.19/0.47      ine: secrecy_specID > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_OineM,type,
% 0.19/0.47      ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.19/0.47      ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.19/0.47      ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.19/0.47      out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.19/0.47      out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_OCollect,type,
% 0.19/0.47      collect: 
% 0.19/0.47        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_Oinsert,type,
% 0.19/0.47      insert: 
% 0.19/0.47        !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_Ois__empty,type,
% 0.19/0.47      is_empty: 
% 0.19/0.47        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_Ois__singleton,type,
% 0.19/0.47      is_singleton: 
% 0.19/0.47        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_Opairwise,type,
% 0.19/0.47      pairwise: 
% 0.19/0.47        !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_Set_Othe__elem,type,
% 0.19/0.47      the_elem: 
% 0.19/0.47        !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.19/0.47      correctCompositionIn: secrecy_specID > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.19/0.47      correc965049635ionLoc: secrecy_specID > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.19/0.47      correc990227761ionOut: secrecy_specID > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OcorrectInOutLoc,type,
% 0.19/0.47      correctInOutLoc: secrecy_specID > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OinStream,type,
% 0.19/0.47      inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_Oins,type,
% 0.19/0.47      ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_Oloc,type,
% 0.19/0.47      loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OlocStream,type,
% 0.19/0.47      locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_Oout,type,
% 0.19/0.47      out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_OoutStream,type,
% 0.19/0.47      outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_inout_Osubcomponents,type,
% 0.19/0.47      subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_c_member,type,
% 0.19/0.47      member: 
% 0.19/0.47        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_v_P,type,
% 0.19/0.47      p: secrecy_specID ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_v_PQ,type,
% 0.19/0.47      pq: secrecy_specID ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_v_Q,type,
% 0.19/0.47      q: secrecy_specID ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_v_ch,type,
% 0.19/0.47      ch: secrecy_chanID ).
% 0.19/0.47  
% 0.19/0.47  thf(sy_v_m,type,
% 0.19/0.47      m: secrecy_Expression ).
% 0.19/0.47  
% 0.19/0.47  % Relevant facts (256)
% 0.19/0.47  thf(fact_0_assms_I2_J,axiom,
% 0.19/0.47      correctCompositionIn @ pq ).
% 0.19/0.47  
% 0.19/0.47  % assms(2)
% 0.19/0.47  thf(fact_1_assms_I4_J,axiom,
% 0.19/0.47      exprChannel @ ch @ m ).
% 0.19/0.47  
% 0.19/0.47  % assms(4)
% 0.19/0.47  thf(fact_2_assms_I3_J,axiom,
% 0.19/0.47      member @ secrecy_chanID @ ch @ ( ins @ p ) ).
% 0.19/0.47  
% 0.19/0.47  % assms(3)
% 0.19/0.47  thf(fact_3_assms_I5_J,axiom,
% 0.19/0.47      ! [X: secrecy_chanID] :
% 0.19/0.47        ( ( member @ secrecy_chanID @ X @ ( ins @ pq ) )
% 0.19/0.47       => ~ ( exprChannel @ X @ m ) ) ).
% 0.19/0.47  
% 0.19/0.47  % assms(5)
% 0.19/0.47  thf(fact_4_assms_I1_J,axiom,
% 0.19/0.47      ( ( subcomponents @ pq )
% 0.19/0.47      = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % assms(1)
% 0.19/0.47  thf(fact_5_locStream__def,axiom,
% 0.19/0.47      ( locStream
% 0.19/0.47      = ( ^ [X2: secrecy_specID] :
% 0.19/0.47            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.19/0.47            @ ( loc @ X2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % locStream_def
% 0.19/0.47  thf(fact_6_correctCompositionIn__L1,axiom,
% 0.19/0.47      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.19/0.47        ( ( ( subcomponents @ PQ )
% 0.19/0.47          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47       => ( ( correctCompositionIn @ PQ )
% 0.19/0.47         => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.19/0.47           => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.19/0.47             => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % correctCompositionIn_L1
% 0.19/0.47  thf(fact_7_correctCompositionIn__L2,axiom,
% 0.19/0.47      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.19/0.47        ( ( ( subcomponents @ PQ )
% 0.19/0.47          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47       => ( ( correctCompositionIn @ PQ )
% 0.19/0.47         => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.19/0.47           => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.19/0.47              | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % correctCompositionIn_L2
% 0.19/0.47  thf(fact_8_correctCompositionIn__prop1,axiom,
% 0.19/0.47      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.19/0.47        ( ( ( subcomponents @ PQ )
% 0.19/0.47          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47       => ( ( correctCompositionIn @ PQ )
% 0.19/0.47         => ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 0.19/0.47           => ( ( member @ secrecy_chanID @ X3 @ ( ins @ P ) )
% 0.19/0.47              | ( member @ secrecy_chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % correctCompositionIn_prop1
% 0.19/0.47  thf(fact_9_singletonI,axiom,
% 0.19/0.47      ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % singletonI
% 0.19/0.47  thf(fact_10_TBtheorem4b__P,axiom,
% 0.19/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.19/0.47        ( ( ineM @ P @ M @ E )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ? [Ch2: secrecy_chanID] :
% 0.19/0.47                  ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 0.19/0.47                  & ( exprChannel @ Ch2 @ E )
% 0.19/0.47                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.19/0.47                  & ( member @ secrecy_chanID @ Ch2 @ M ) )
% 0.19/0.47             => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4b_P
% 0.19/0.47  thf(fact_11_TBtheorem4b__PQ,axiom,
% 0.19/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.19/0.47        ( ( ( ineM @ P @ M @ E )
% 0.19/0.47          | ( ineM @ Q @ M @ E ) )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ? [Ch2: secrecy_chanID] :
% 0.19/0.47                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.19/0.47                    | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.19/0.47                  & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.19/0.47                  & ( exprChannel @ Ch2 @ E )
% 0.19/0.47                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.19/0.47             => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4b_PQ
% 0.19/0.47  thf(fact_12_TBlemma3b,axiom,
% 0.19/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.19/0.47        ( ~ ( ineM @ P @ M @ E )
% 0.19/0.47       => ( ~ ( ineM @ Q @ M @ E )
% 0.19/0.47         => ( ( ( subcomponents @ PQ )
% 0.19/0.47              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47           => ( ( correctCompositionIn @ PQ )
% 0.19/0.47             => ( ( member @ secrecy_chanID @ Ch @ M )
% 0.19/0.47               => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.19/0.47                 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBlemma3b
% 0.19/0.47  thf(fact_13_inStream__def,axiom,
% 0.19/0.47      ( inStream
% 0.19/0.47      = ( ^ [X2: secrecy_specID] :
% 0.19/0.47            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.19/0.47            @ ( ins @ X2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % inStream_def
% 0.19/0.47  thf(fact_14_insertCI,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.19/0.47        ( ( ~ ( member @ A @ A2 @ B )
% 0.19/0.47         => ( A2 = B2 ) )
% 0.19/0.47       => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insertCI
% 0.19/0.47  thf(fact_15_insert__iff,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.19/0.47        ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.19/0.47        = ( ( A2 = B2 )
% 0.19/0.47          | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_iff
% 0.19/0.47  thf(fact_16_insert__absorb2,axiom,
% 0.19/0.47      ! [A: $tType,X3: A,A3: set @ A] :
% 0.19/0.47        ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A3 ) )
% 0.19/0.47        = ( insert @ A @ X3 @ A3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_absorb2
% 0.19/0.47  thf(fact_17_empty__iff,axiom,
% 0.19/0.47      ! [A: $tType,C: A] :
% 0.19/0.47        ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % empty_iff
% 0.19/0.47  thf(fact_18_all__not__in__conv,axiom,
% 0.19/0.47      ! [A: $tType,A3: set @ A] :
% 0.19/0.47        ( ( ! [X2: A] :
% 0.19/0.47              ~ ( member @ A @ X2 @ A3 ) )
% 0.19/0.47        = ( A3
% 0.19/0.47          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % all_not_in_conv
% 0.19/0.47  thf(fact_19_Collect__empty__eq,axiom,
% 0.19/0.47      ! [A: $tType,P: A > $o] :
% 0.19/0.47        ( ( ( collect @ A @ P )
% 0.19/0.47          = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47        = ( ! [X2: A] :
% 0.19/0.47              ~ ( P @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Collect_empty_eq
% 0.19/0.47  thf(fact_20_empty__Collect__eq,axiom,
% 0.19/0.47      ! [A: $tType,P: A > $o] :
% 0.19/0.47        ( ( ( bot_bot @ ( set @ A ) )
% 0.19/0.47          = ( collect @ A @ P ) )
% 0.19/0.47        = ( ! [X2: A] :
% 0.19/0.47              ~ ( P @ X2 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % empty_Collect_eq
% 0.19/0.47  thf(fact_21_ineM__def,axiom,
% 0.19/0.47      ( ineM
% 0.19/0.47      = ( ^ [SP: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.19/0.47          ? [Ch3: secrecy_chanID] :
% 0.19/0.47            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.19/0.47            & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.19/0.47            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ineM_def
% 0.19/0.47  thf(fact_22_ineM__L1,axiom,
% 0.19/0.47      ! [Ch: secrecy_chanID,M: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.19/0.47        ( ( member @ secrecy_chanID @ Ch @ M )
% 0.19/0.47       => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.19/0.47         => ( ( exprChannel @ Ch @ E )
% 0.19/0.47           => ( ineM @ P @ M @ E ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ineM_L1
% 0.19/0.47  thf(fact_23_ex__in__conv,axiom,
% 0.19/0.47      ! [A: $tType,A3: set @ A] :
% 0.19/0.47        ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.19/0.47        = ( A3
% 0.19/0.47         != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ex_in_conv
% 0.19/0.47  thf(fact_24_equals0I,axiom,
% 0.19/0.47      ! [A: $tType,A3: set @ A] :
% 0.19/0.47        ( ! [Y2: A] :
% 0.19/0.47            ~ ( member @ A @ Y2 @ A3 )
% 0.19/0.47       => ( A3
% 0.19/0.47          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % equals0I
% 0.19/0.47  thf(fact_25_equals0D,axiom,
% 0.19/0.47      ! [A: $tType,A3: set @ A,A2: A] :
% 0.19/0.47        ( ( A3
% 0.19/0.47          = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47       => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % equals0D
% 0.19/0.47  thf(fact_26_emptyE,axiom,
% 0.19/0.47      ! [A: $tType,A2: A] :
% 0.19/0.47        ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % emptyE
% 0.19/0.47  thf(fact_27_mk__disjoint__insert,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47        ( ( member @ A @ A2 @ A3 )
% 0.19/0.47       => ? [B3: set @ A] :
% 0.19/0.47            ( ( A3
% 0.19/0.47              = ( insert @ A @ A2 @ B3 ) )
% 0.19/0.47            & ~ ( member @ A @ A2 @ B3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % mk_disjoint_insert
% 0.19/0.47  thf(fact_28_insert__commute,axiom,
% 0.19/0.47      ! [A: $tType,X3: A,Y3: A,A3: set @ A] :
% 0.19/0.47        ( ( insert @ A @ X3 @ ( insert @ A @ Y3 @ A3 ) )
% 0.19/0.47        = ( insert @ A @ Y3 @ ( insert @ A @ X3 @ A3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_commute
% 0.19/0.47  thf(fact_29_insert__eq__iff,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,A3: set @ A,B2: A,B: set @ A] :
% 0.19/0.47        ( ~ ( member @ A @ A2 @ A3 )
% 0.19/0.47       => ( ~ ( member @ A @ B2 @ B )
% 0.19/0.47         => ( ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47              = ( insert @ A @ B2 @ B ) )
% 0.19/0.47            = ( ( ( A2 = B2 )
% 0.19/0.47               => ( A3 = B ) )
% 0.19/0.47              & ( ( A2 != B2 )
% 0.19/0.47               => ? [C2: set @ A] :
% 0.19/0.47                    ( ( A3
% 0.19/0.47                      = ( insert @ A @ B2 @ C2 ) )
% 0.19/0.47                    & ~ ( member @ A @ B2 @ C2 )
% 0.19/0.47                    & ( B
% 0.19/0.47                      = ( insert @ A @ A2 @ C2 ) )
% 0.19/0.47                    & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_eq_iff
% 0.19/0.47  thf(fact_30_insert__absorb,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47        ( ( member @ A @ A2 @ A3 )
% 0.19/0.47       => ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47          = A3 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_absorb
% 0.19/0.47  thf(fact_31_insert__ident,axiom,
% 0.19/0.47      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.19/0.47        ( ~ ( member @ A @ X3 @ A3 )
% 0.19/0.47       => ( ~ ( member @ A @ X3 @ B )
% 0.19/0.47         => ( ( ( insert @ A @ X3 @ A3 )
% 0.19/0.47              = ( insert @ A @ X3 @ B ) )
% 0.19/0.47            = ( A3 = B ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_ident
% 0.19/0.47  thf(fact_32_Set_Oset__insert,axiom,
% 0.19/0.47      ! [A: $tType,X3: A,A3: set @ A] :
% 0.19/0.47        ( ( member @ A @ X3 @ A3 )
% 0.19/0.47       => ~ ! [B3: set @ A] :
% 0.19/0.47              ( ( A3
% 0.19/0.47                = ( insert @ A @ X3 @ B3 ) )
% 0.19/0.47             => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Set.set_insert
% 0.19/0.47  thf(fact_33_insertI2,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.19/0.47        ( ( member @ A @ A2 @ B )
% 0.19/0.47       => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insertI2
% 0.19/0.47  thf(fact_34_insertI1,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insertI1
% 0.19/0.47  thf(fact_35_insertE,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.19/0.47        ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.19/0.47       => ( ( A2 != B2 )
% 0.19/0.47         => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insertE
% 0.19/0.47  thf(fact_36_TBtheorem3b,axiom,
% 0.19/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.19/0.47        ( ~ ( ineM @ P @ M @ E )
% 0.19/0.47       => ( ~ ( ineM @ Q @ M @ E )
% 0.19/0.47         => ( ( ( subcomponents @ PQ )
% 0.19/0.47              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47           => ( ( correctCompositionIn @ PQ )
% 0.19/0.47             => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem3b
% 0.19/0.47  thf(fact_37_TBtheorem1b,axiom,
% 0.19/0.47      ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.19/0.47        ( ( ineM @ PQ @ M @ E )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ( ineM @ P @ M @ E )
% 0.19/0.47              | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem1b
% 0.19/0.47  thf(fact_38_singleton__inject,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B2: A] :
% 0.19/0.47        ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.47          = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47       => ( A2 = B2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % singleton_inject
% 0.19/0.47  thf(fact_39_insert__not__empty,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,A3: set @ A] :
% 0.19/0.47        ( ( insert @ A @ A2 @ A3 )
% 0.19/0.47       != ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % insert_not_empty
% 0.19/0.47  thf(fact_40_doubleton__eq__iff,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,B2: A,C: A,D: A] :
% 0.19/0.47        ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47          = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.19/0.47        = ( ( ( A2 = C )
% 0.19/0.47            & ( B2 = D ) )
% 0.19/0.47          | ( ( A2 = D )
% 0.19/0.47            & ( B2 = C ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % doubleton_eq_iff
% 0.19/0.47  thf(fact_41_singleton__iff,axiom,
% 0.19/0.47      ! [A: $tType,B2: A,A2: A] :
% 0.19/0.47        ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47        = ( B2 = A2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % singleton_iff
% 0.19/0.47  thf(fact_42_singletonD,axiom,
% 0.19/0.47      ! [A: $tType,B2: A,A2: A] :
% 0.19/0.47        ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47       => ( B2 = A2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % singletonD
% 0.19/0.47  thf(fact_43_TBtheorem4b__notP1,axiom,
% 0.19/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.19/0.47        ( ( ineM @ P @ M @ E )
% 0.19/0.47       => ( ~ ( ineM @ Q @ M @ E )
% 0.19/0.47         => ( ( ( subcomponents @ PQ )
% 0.19/0.47              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47           => ( ( correctCompositionIn @ PQ )
% 0.19/0.47             => ( ? [Ch2: secrecy_chanID] :
% 0.19/0.47                    ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.19/0.47                    & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.19/0.47                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.19/0.47               => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4b_notP1
% 0.19/0.47  thf(fact_44_TBtheorem4b__notPQ,axiom,
% 0.19/0.47      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.19/0.47        ( ( ( subcomponents @ PQ )
% 0.19/0.47          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47       => ( ( correctCompositionIn @ PQ )
% 0.19/0.47         => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.19/0.47           => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.19/0.47             => ( ! [X4: secrecy_chanID] :
% 0.19/0.47                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.19/0.47                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.19/0.47               => ( ! [X4: secrecy_chanID] :
% 0.19/0.47                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.19/0.47                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.19/0.47                 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4b_notPQ
% 0.19/0.47  thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.47      ! [A: $tType,A2: A,P: A > $o] :
% 0.19/0.47        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.19/0.47        = ( P @ A2 ) ) ).
% 0.19/0.47  
% 0.19/0.47  % mem_Collect_eq
% 0.19/0.47  thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.47      ! [A: $tType,A3: set @ A] :
% 0.19/0.47        ( ( collect @ A
% 0.19/0.47          @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.19/0.47        = A3 ) ).
% 0.19/0.47  
% 0.19/0.47  % Collect_mem_eq
% 0.19/0.47  thf(fact_47_Collect__cong,axiom,
% 0.19/0.47      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.47        ( ! [X4: A] :
% 0.19/0.47            ( ( P @ X4 )
% 0.19/0.47            = ( Q @ X4 ) )
% 0.19/0.47       => ( ( collect @ A @ P )
% 0.19/0.47          = ( collect @ A @ Q ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % Collect_cong
% 0.19/0.47  thf(fact_48_ext,axiom,
% 0.19/0.47      ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 0.19/0.47        ( ! [X4: A] :
% 0.19/0.47            ( ( F @ X4 )
% 0.19/0.47            = ( G @ X4 ) )
% 0.19/0.47       => ( F = G ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ext
% 0.19/0.47  thf(fact_49_TBtheorem4b__notP2,axiom,
% 0.19/0.47      ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.19/0.47        ( ~ ( ineM @ Q @ M @ E )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.19/0.47             => ( ! [X4: secrecy_chanID] :
% 0.19/0.47                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.19/0.47                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.19/0.47               => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4b_notP2
% 0.19/0.47  thf(fact_50_the__elem__eq,axiom,
% 0.19/0.47      ! [A: $tType,X3: A] :
% 0.19/0.47        ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.47        = X3 ) ).
% 0.19/0.47  
% 0.19/0.47  % the_elem_eq
% 0.19/0.47  thf(fact_51_bot__apply,axiom,
% 0.19/0.47      ! [C3: $tType,D2: $tType] :
% 0.19/0.47        ( ( bot @ C3 )
% 0.19/0.47       => ( ( bot_bot @ ( D2 > C3 ) )
% 0.19/0.47          = ( ^ [X2: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % bot_apply
% 0.19/0.47  thf(fact_52_TBtheorem4a__PQ,axiom,
% 0.19/0.47      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.19/0.47        ( ( ( ine @ P @ E )
% 0.19/0.47          | ( ine @ Q @ E ) )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ? [Ch2: secrecy_chanID] :
% 0.19/0.47                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.19/0.47                    | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.19/0.47                  & ( exprChannel @ Ch2 @ E )
% 0.19/0.47                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.19/0.47             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4a_PQ
% 0.19/0.47  thf(fact_53_TBtheorem4a__P,axiom,
% 0.19/0.47      ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.19/0.47        ( ( ine @ P @ E )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ? [Ch2: secrecy_chanID] :
% 0.19/0.47                  ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.19/0.47                  & ( exprChannel @ Ch2 @ E )
% 0.19/0.47                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.19/0.47             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4a_P
% 0.19/0.47  thf(fact_54_is__singletonI,axiom,
% 0.19/0.47      ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % is_singletonI
% 0.19/0.47  thf(fact_55_TBtheorem4a__empty,axiom,
% 0.19/0.47      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.19/0.47        ( ( ( ine @ P @ E )
% 0.19/0.47          | ( ine @ Q @ E ) )
% 0.19/0.47       => ( ( ( subcomponents @ PQ )
% 0.19/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.19/0.47         => ( ( correctCompositionIn @ PQ )
% 0.19/0.47           => ( ( ( loc @ PQ )
% 0.19/0.47                = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.19/0.47             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % TBtheorem4a_empty
% 0.19/0.47  thf(fact_56_ine__exprChannelSingle__def,axiom,
% 0.19/0.47      ( ine_ex1303305700Single
% 0.19/0.47      = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.19/0.47            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.19/0.47            & ( exprChannel @ Ch3 @ E2 )
% 0.19/0.47            & ! [X2: secrecy_chanID,T: nat] :
% 0.19/0.47                ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.19/0.47                  & ( X2 != Ch3 ) )
% 0.19/0.47               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ine_exprChannelSingle_def
% 0.19/0.47  thf(fact_57_ine__empty__exprChannelSet,axiom,
% 0.19/0.47      ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.19/0.47        ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.19/0.47       => ( ( ChSet
% 0.19/0.47            = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.19/0.47         => ~ ( ine @ P @ E ) ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ine_empty_exprChannelSet
% 0.19/0.47  thf(fact_58_ine__exprChannelSet__Single,axiom,
% 0.19/0.47      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.19/0.47        ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.19/0.47       => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ine_exprChannelSet_Single
% 0.19/0.47  thf(fact_59_ine__exprChannelSingle__Set,axiom,
% 0.19/0.47      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.19/0.47        ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.19/0.47       => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.19/0.47  
% 0.19/0.47  % ine_exprChannelSingle_Set
% 0.19/0.47  thf(fact_60_ine__nonempty__exprChannelSet,axiom,
% 0.19/0.47      ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.19/0.47        ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.19/0.47       => ( ( ChSet
% 0.19/0.47           != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/0.47         => ( ine @ P @ E ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % ine_nonempty_exprChannelSet
% 0.32/0.47  thf(fact_61_bot__set__def,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( bot_bot @ ( set @ A ) )
% 0.32/0.47        = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % bot_set_def
% 0.32/0.47  thf(fact_62_not__ine__ineM,axiom,
% 0.32/0.47      ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.32/0.47        ( ~ ( ine @ P @ E )
% 0.32/0.47       => ~ ( ineM @ P @ M @ E ) ) ).
% 0.32/0.47  
% 0.32/0.47  % not_ine_ineM
% 0.32/0.47  thf(fact_63_ineM__ine,axiom,
% 0.32/0.47      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/0.47        ( ( ineM @ P @ M @ E )
% 0.32/0.47       => ( ine @ P @ E ) ) ).
% 0.32/0.47  
% 0.32/0.47  % ineM_ine
% 0.32/0.47  thf(fact_64_is__singleton__the__elem,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( is_singleton @ A )
% 0.32/0.47        = ( ^ [A4: set @ A] :
% 0.32/0.47              ( A4
% 0.32/0.47              = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % is_singleton_the_elem
% 0.32/0.47  thf(fact_65_ine__def,axiom,
% 0.32/0.47      ( ine
% 0.32/0.47      = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.32/0.47          ? [Ch3: secrecy_chanID] :
% 0.32/0.47            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.32/0.47            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % ine_def
% 0.32/0.47  thf(fact_66_ine__ins__neg1,axiom,
% 0.32/0.47      ! [P: secrecy_specID,M3: secrecy_Expression,X3: secrecy_chanID] :
% 0.32/0.47        ( ~ ( ine @ P @ M3 )
% 0.32/0.47       => ( ( exprChannel @ X3 @ M3 )
% 0.32/0.47         => ~ ( member @ secrecy_chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % ine_ins_neg1
% 0.32/0.47  thf(fact_67_is__singletonI_H,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A] :
% 0.32/0.47        ( ( A3
% 0.32/0.47         != ( bot_bot @ ( set @ A ) ) )
% 0.32/0.47       => ( ! [X4: A,Y2: A] :
% 0.32/0.47              ( ( member @ A @ X4 @ A3 )
% 0.32/0.47             => ( ( member @ A @ Y2 @ A3 )
% 0.32/0.47               => ( X4 = Y2 ) ) )
% 0.32/0.47         => ( is_singleton @ A @ A3 ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % is_singletonI'
% 0.32/0.47  thf(fact_68_bot__fun__def,axiom,
% 0.32/0.47      ! [B4: $tType,A: $tType] :
% 0.32/0.47        ( ( bot @ B4 )
% 0.32/0.47       => ( ( bot_bot @ ( A > B4 ) )
% 0.32/0.47          = ( ^ [X2: A] : ( bot_bot @ B4 ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % bot_fun_def
% 0.32/0.47  thf(fact_69_TBtheorem4a__notP2,axiom,
% 0.32/0.47      ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/0.47        ( ~ ( ine @ Q @ E )
% 0.32/0.47       => ( ( ( subcomponents @ PQ )
% 0.32/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47         => ( ( correctCompositionIn @ PQ )
% 0.32/0.47           => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.32/0.47             => ( ! [X4: secrecy_chanID] :
% 0.32/0.47                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/0.47                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.47               => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem4a_notP2
% 0.32/0.47  thf(fact_70_TBtheorem4a__notPQ,axiom,
% 0.32/0.47      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.32/0.47        ( ( ( subcomponents @ PQ )
% 0.32/0.47          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47       => ( ( correctCompositionIn @ PQ )
% 0.32/0.47         => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.32/0.47           => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/0.47             => ( ! [X4: secrecy_chanID] :
% 0.32/0.47                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/0.47                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.47               => ( ! [X4: secrecy_chanID] :
% 0.32/0.47                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/0.47                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.47                 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem4a_notPQ
% 0.32/0.47  thf(fact_71_TBtheorem4a__notP1,axiom,
% 0.32/0.47      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.47        ( ( ine @ P @ E )
% 0.32/0.47       => ( ~ ( ine @ Q @ E )
% 0.32/0.47         => ( ( ( subcomponents @ PQ )
% 0.32/0.47              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47           => ( ( correctCompositionIn @ PQ )
% 0.32/0.47             => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.47                    ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.32/0.47                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.47               => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem4a_notP1
% 0.32/0.47  thf(fact_72_ine__exprChannelSet__def,axiom,
% 0.32/0.47      ( ine_exprChannelSet
% 0.32/0.47      = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/0.47            ( ! [X2: secrecy_chanID] :
% 0.32/0.47                ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/0.47               => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.32/0.47                  & ( exprChannel @ X2 @ E2 ) ) )
% 0.32/0.47            & ! [X2: secrecy_chanID] :
% 0.32/0.47                ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/0.47                  & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 0.32/0.47               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % ine_exprChannelSet_def
% 0.32/0.47  thf(fact_73_is__singletonE,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A] :
% 0.32/0.47        ( ( is_singleton @ A @ A3 )
% 0.32/0.47       => ~ ! [X4: A] :
% 0.32/0.47              ( A3
% 0.32/0.47             != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % is_singletonE
% 0.32/0.47  thf(fact_74_is__singleton__def,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( is_singleton @ A )
% 0.32/0.47        = ( ^ [A4: set @ A] :
% 0.32/0.47            ? [X2: A] :
% 0.32/0.47              ( A4
% 0.32/0.47              = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % is_singleton_def
% 0.32/0.47  thf(fact_75_TBtheorem1a,axiom,
% 0.32/0.47      ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/0.47        ( ( ine @ PQ @ E )
% 0.32/0.47       => ( ( ( subcomponents @ PQ )
% 0.32/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47         => ( ( correctCompositionIn @ PQ )
% 0.32/0.47           => ( ( ine @ P @ E )
% 0.32/0.47              | ( ine @ Q @ E ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem1a
% 0.32/0.47  thf(fact_76_TBtheorem3a,axiom,
% 0.32/0.47      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.47        ( ~ ( ine @ P @ E )
% 0.32/0.47       => ( ~ ( ine @ Q @ E )
% 0.32/0.47         => ( ( ( subcomponents @ PQ )
% 0.32/0.47              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47           => ( ( correctCompositionIn @ PQ )
% 0.32/0.47             => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem3a
% 0.32/0.47  thf(fact_77_subcomponents__loc,axiom,
% 0.32/0.47      ! [X3: secrecy_specID] :
% 0.32/0.47        ( ( correc965049635ionLoc @ X3 )
% 0.32/0.47       => ( ( ( subcomponents @ X3 )
% 0.32/0.47            = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.32/0.47         => ( ( loc @ X3 )
% 0.32/0.47            = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % subcomponents_loc
% 0.32/0.47  thf(fact_78_Set_Ois__empty__def,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( is_empty @ A )
% 0.32/0.47        = ( ^ [A4: set @ A] :
% 0.32/0.47              ( A4
% 0.32/0.47              = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % Set.is_empty_def
% 0.32/0.47  thf(fact_79_TBtheorem5a__empty,axiom,
% 0.32/0.47      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.47        ( ( ( eout @ P @ E )
% 0.32/0.47          | ( eout @ Q @ E ) )
% 0.32/0.47       => ( ( ( subcomponents @ PQ )
% 0.32/0.47            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.47         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.47           => ( ( ( loc @ PQ )
% 0.32/0.47                = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/0.47             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % TBtheorem5a_empty
% 0.32/0.47  thf(fact_80_bot__empty__eq,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( bot_bot @ ( A > $o ) )
% 0.32/0.47        = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % bot_empty_eq
% 0.32/0.47  thf(fact_81_Collect__empty__eq__bot,axiom,
% 0.32/0.47      ! [A: $tType,P: A > $o] :
% 0.32/0.47        ( ( ( collect @ A @ P )
% 0.32/0.47          = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.47        = ( P
% 0.32/0.47          = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % Collect_empty_eq_bot
% 0.32/0.47  thf(fact_82_pairwise__singleton,axiom,
% 0.32/0.47      ! [A: $tType,P: A > A > $o,A3: A] : ( pairwise @ A @ P @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % pairwise_singleton
% 0.32/0.47  thf(fact_83_singleton__insert__inj__eq,axiom,
% 0.32/0.47      ! [A: $tType,B2: A,A2: A,A3: set @ A] :
% 0.32/0.47        ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.47          = ( insert @ A @ A2 @ A3 ) )
% 0.32/0.47        = ( ( A2 = B2 )
% 0.32/0.47          & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % singleton_insert_inj_eq
% 0.32/0.47  thf(fact_84_order__refl,axiom,
% 0.32/0.47      ! [A: $tType] :
% 0.32/0.47        ( ( preorder @ A )
% 0.32/0.47       => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.32/0.47  
% 0.32/0.47  % order_refl
% 0.32/0.47  thf(fact_85_subsetI,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.47        ( ! [X4: A] :
% 0.32/0.47            ( ( member @ A @ X4 @ A3 )
% 0.32/0.47           => ( member @ A @ X4 @ B ) )
% 0.32/0.47       => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/0.47  
% 0.32/0.47  % subsetI
% 0.32/0.47  thf(fact_86_subset__antisym,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.47        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.47       => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/0.47         => ( A3 = B ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % subset_antisym
% 0.32/0.47  thf(fact_87_empty__subsetI,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.32/0.47  
% 0.32/0.47  % empty_subsetI
% 0.32/0.47  thf(fact_88_subset__empty,axiom,
% 0.32/0.47      ! [A: $tType,A3: set @ A] :
% 0.32/0.47        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.47        = ( A3
% 0.32/0.47          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % subset_empty
% 0.32/0.47  thf(fact_89_insert__subset,axiom,
% 0.32/0.47      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/0.47        ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B )
% 0.32/0.47        = ( ( member @ A @ X3 @ B )
% 0.32/0.47          & ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % insert_subset
% 0.32/0.47  thf(fact_90_singleton__insert__inj__eq_H,axiom,
% 0.32/0.47      ! [A: $tType,A2: A,A3: set @ A,B2: A] :
% 0.32/0.47        ( ( ( insert @ A @ A2 @ A3 )
% 0.32/0.47          = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.47        = ( ( A2 = B2 )
% 0.32/0.47          & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % singleton_insert_inj_eq'
% 0.32/0.47  thf(fact_91_le__funD,axiom,
% 0.32/0.47      ! [B4: $tType,A: $tType] :
% 0.32/0.47        ( ( ord @ B4 )
% 0.32/0.47       => ! [F: A > B4,G: A > B4,X3: A] :
% 0.32/0.47            ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.32/0.47           => ( ord_less_eq @ B4 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % le_funD
% 0.32/0.47  thf(fact_92_le__funE,axiom,
% 0.32/0.47      ! [B4: $tType,A: $tType] :
% 0.32/0.47        ( ( ord @ B4 )
% 0.32/0.47       => ! [F: A > B4,G: A > B4,X3: A] :
% 0.32/0.47            ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.32/0.47           => ( ord_less_eq @ B4 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % le_funE
% 0.32/0.47  thf(fact_93_le__funI,axiom,
% 0.32/0.47      ! [B4: $tType,A: $tType] :
% 0.32/0.47        ( ( ord @ B4 )
% 0.32/0.47       => ! [F: A > B4,G: A > B4] :
% 0.32/0.47            ( ! [X4: A] : ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.32/0.47           => ( ord_less_eq @ ( A > B4 ) @ F @ G ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % le_funI
% 0.32/0.47  thf(fact_94_le__fun__def,axiom,
% 0.32/0.47      ! [B4: $tType,A: $tType] :
% 0.32/0.47        ( ( ord @ B4 )
% 0.32/0.47       => ( ( ord_less_eq @ ( A > B4 ) )
% 0.32/0.47          = ( ^ [F2: A > B4,G2: A > B4] :
% 0.32/0.47              ! [X2: A] : ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % le_fun_def
% 0.32/0.47  thf(fact_95_order__subst1,axiom,
% 0.32/0.47      ! [A: $tType,B4: $tType] :
% 0.32/0.47        ( ( ( order @ B4 )
% 0.32/0.47          & ( order @ A ) )
% 0.32/0.47       => ! [A2: A,F: B4 > A,B2: B4,C: B4] :
% 0.32/0.47            ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.32/0.47           => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.32/0.47             => ( ! [X4: B4,Y2: B4] :
% 0.32/0.47                    ( ( ord_less_eq @ B4 @ X4 @ Y2 )
% 0.32/0.47                   => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/0.47               => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/0.47  
% 0.32/0.47  % order_subst1
% 0.32/0.47  thf(fact_96_order__subst2,axiom,
% 0.32/0.47      ! [A: $tType,C3: $tType] :
% 0.32/0.47        ( ( ( order @ C3 )
% 0.32/0.47          & ( order @ A ) )
% 0.32/0.47       => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.32/0.47            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.47           => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 0.32/0.47             => ( ! [X4: A,Y2: A] :
% 0.32/0.48                    ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.32/0.48                   => ( ord_less_eq @ C3 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/0.48               => ( ord_less_eq @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % order_subst2
% 0.32/0.48  thf(fact_97_ord__eq__le__subst,axiom,
% 0.32/0.48      ! [A: $tType,B4: $tType] :
% 0.32/0.48        ( ( ( ord @ B4 )
% 0.32/0.48          & ( ord @ A ) )
% 0.32/0.48       => ! [A2: A,F: B4 > A,B2: B4,C: B4] :
% 0.32/0.48            ( ( A2
% 0.32/0.48              = ( F @ B2 ) )
% 0.32/0.48           => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.32/0.48             => ( ! [X4: B4,Y2: B4] :
% 0.32/0.48                    ( ( ord_less_eq @ B4 @ X4 @ Y2 )
% 0.32/0.48                   => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/0.48               => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ord_eq_le_subst
% 0.32/0.48  thf(fact_98_ord__le__eq__subst,axiom,
% 0.32/0.48      ! [A: $tType,B4: $tType] :
% 0.32/0.48        ( ( ( ord @ B4 )
% 0.32/0.48          & ( ord @ A ) )
% 0.32/0.48       => ! [A2: A,B2: A,F: A > B4,C: B4] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48           => ( ( ( F @ B2 )
% 0.32/0.48                = C )
% 0.32/0.48             => ( ! [X4: A,Y2: A] :
% 0.32/0.48                    ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.32/0.48                   => ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/0.48               => ( ord_less_eq @ B4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ord_le_eq_subst
% 0.32/0.48  thf(fact_99_eq__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/0.48          = ( ^ [X2: A,Y4: A] :
% 0.32/0.48                ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.32/0.48                & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % eq_iff
% 0.32/0.48  thf(fact_100_antisym,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/0.48             => ( X3 = Y3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % antisym
% 0.32/0.48  thf(fact_101_linear,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( linorder @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48            | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % linear
% 0.32/0.48  thf(fact_102_eq__refl,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( preorder @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( X3 = Y3 )
% 0.32/0.48           => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % eq_refl
% 0.32/0.48  thf(fact_103_le__cases,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( linorder @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48           => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_cases
% 0.32/0.48  thf(fact_104_order_Otrans,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [A2: A,B2: A,C: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/0.48             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % order.trans
% 0.32/0.48  thf(fact_105_le__cases3,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( linorder @ A )
% 0.32/0.48       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/0.48            ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48             => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.32/0.48           => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/0.48               => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.32/0.48             => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.32/0.48                 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.32/0.48               => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.32/0.48                   => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.32/0.48                 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.32/0.48                     => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.32/0.48                   => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.32/0.48                       => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_cases3
% 0.32/0.48  thf(fact_106_antisym__conv,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [Y3: A,X3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48              = ( X3 = Y3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % antisym_conv
% 0.32/0.48  thf(fact_107_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/0.48          = ( ^ [A5: A,B5: A] :
% 0.32/0.48                ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.32/0.48                & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % order_class.order.eq_iff
% 0.32/0.48  thf(fact_108_ord__eq__le__trans,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ord @ A )
% 0.32/0.48       => ! [A2: A,B2: A,C: A] :
% 0.32/0.48            ( ( A2 = B2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/0.48             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ord_eq_le_trans
% 0.32/0.48  thf(fact_109_ord__le__eq__trans,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ord @ A )
% 0.32/0.48       => ! [A2: A,B2: A,C: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48           => ( ( B2 = C )
% 0.32/0.48             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ord_le_eq_trans
% 0.32/0.48  thf(fact_110_order__class_Oorder_Oantisym,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [A2: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48             => ( A2 = B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % order_class.order.antisym
% 0.32/0.48  thf(fact_111_order__trans,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( preorder @ A )
% 0.32/0.48       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.32/0.48             => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % order_trans
% 0.32/0.48  thf(fact_112_dual__order_Orefl,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % dual_order.refl
% 0.32/0.48  thf(fact_113_linorder__wlog,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( linorder @ A )
% 0.32/0.48       => ! [P: A > A > $o,A2: A,B2: A] :
% 0.32/0.48            ( ! [A6: A,B6: A] :
% 0.32/0.48                ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.32/0.48               => ( P @ A6 @ B6 ) )
% 0.32/0.48           => ( ! [A6: A,B6: A] :
% 0.32/0.48                  ( ( P @ B6 @ A6 )
% 0.32/0.48                 => ( P @ A6 @ B6 ) )
% 0.32/0.48             => ( P @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % linorder_wlog
% 0.32/0.48  thf(fact_114_dual__order_Otrans,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [B2: A,A2: A,C: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ C @ B2 )
% 0.32/0.48             => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % dual_order.trans
% 0.32/0.48  thf(fact_115_dual__order_Oeq__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/0.48          = ( ^ [A5: A,B5: A] :
% 0.32/0.48                ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.32/0.48                & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % dual_order.eq_iff
% 0.32/0.48  thf(fact_116_dual__order_Oantisym,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order @ A )
% 0.32/0.48       => ! [B2: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48             => ( A2 = B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % dual_order.antisym
% 0.32/0.48  thf(fact_117_in__mono,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,X3: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48       => ( ( member @ A @ X3 @ A3 )
% 0.32/0.48         => ( member @ A @ X3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % in_mono
% 0.32/0.48  thf(fact_118_subsetD,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,C: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48       => ( ( member @ A @ C @ A3 )
% 0.32/0.48         => ( member @ A @ C @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subsetD
% 0.32/0.48  thf(fact_119_equalityE,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( A3 = B )
% 0.32/0.48       => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48           => ~ ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % equalityE
% 0.32/0.48  thf(fact_120_pairwiseD,axiom,
% 0.32/0.48      ! [A: $tType,R: A > A > $o,S: set @ A,X3: A,Y3: A] :
% 0.32/0.48        ( ( pairwise @ A @ R @ S )
% 0.32/0.48       => ( ( member @ A @ X3 @ S )
% 0.32/0.48         => ( ( member @ A @ Y3 @ S )
% 0.32/0.48           => ( ( X3 != Y3 )
% 0.32/0.48             => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwiseD
% 0.32/0.48  thf(fact_121_pairwiseI,axiom,
% 0.32/0.48      ! [A: $tType,S: set @ A,R: A > A > $o] :
% 0.32/0.48        ( ! [X4: A,Y2: A] :
% 0.32/0.48            ( ( member @ A @ X4 @ S )
% 0.32/0.48           => ( ( member @ A @ Y2 @ S )
% 0.32/0.48             => ( ( X4 != Y2 )
% 0.32/0.48               => ( R @ X4 @ Y2 ) ) ) )
% 0.32/0.48       => ( pairwise @ A @ R @ S ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwiseI
% 0.32/0.48  thf(fact_122_subset__eq,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/0.48        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/0.48            ! [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ A4 )
% 0.32/0.48             => ( member @ A @ X2 @ B7 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_eq
% 0.32/0.48  thf(fact_123_equalityD1,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( A3 = B )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % equalityD1
% 0.32/0.48  thf(fact_124_equalityD2,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( A3 = B )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % equalityD2
% 0.32/0.48  thf(fact_125_subset__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/0.48        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/0.48            ! [T: A] :
% 0.32/0.48              ( ( member @ A @ T @ A4 )
% 0.32/0.48             => ( member @ A @ T @ B7 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_iff
% 0.32/0.48  thf(fact_126_subset__refl,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_refl
% 0.32/0.48  thf(fact_127_Collect__mono,axiom,
% 0.32/0.48      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48        ( ! [X4: A] :
% 0.32/0.48            ( ( P @ X4 )
% 0.32/0.48           => ( Q @ X4 ) )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Collect_mono
% 0.32/0.48  thf(fact_128_pairwise__def,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( pairwise @ A )
% 0.32/0.48        = ( ^ [R2: A > A > $o,S2: set @ A] :
% 0.32/0.48            ! [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ S2 )
% 0.32/0.48             => ! [Y4: A] :
% 0.32/0.48                  ( ( member @ A @ Y4 @ S2 )
% 0.32/0.48                 => ( ( X2 != Y4 )
% 0.32/0.48                   => ( R2 @ X2 @ Y4 ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwise_def
% 0.32/0.48  thf(fact_129_subset__trans,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.32/0.48         => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_trans
% 0.32/0.48  thf(fact_130_pairwise__mono,axiom,
% 0.32/0.48      ! [A: $tType,P: A > A > $o,A3: set @ A,Q: A > A > $o,B: set @ A] :
% 0.32/0.48        ( ( pairwise @ A @ P @ A3 )
% 0.32/0.48       => ( ! [X4: A,Y2: A] :
% 0.32/0.48              ( ( P @ X4 @ Y2 )
% 0.32/0.48             => ( Q @ X4 @ Y2 ) )
% 0.32/0.48         => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/0.48           => ( pairwise @ A @ Q @ B ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwise_mono
% 0.32/0.48  thf(fact_131_set__eq__subset,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.32/0.48        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/0.48              ( ( ord_less_eq @ ( set @ A ) @ A4 @ B7 )
% 0.32/0.48              & ( ord_less_eq @ ( set @ A ) @ B7 @ A4 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % set_eq_subset
% 0.32/0.48  thf(fact_132_pairwise__subset,axiom,
% 0.32/0.48      ! [A: $tType,P: A > A > $o,S: set @ A,T2: set @ A] :
% 0.32/0.48        ( ( pairwise @ A @ P @ S )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ T2 @ S )
% 0.32/0.48         => ( pairwise @ A @ P @ T2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwise_subset
% 0.32/0.48  thf(fact_133_Collect__mono__iff,axiom,
% 0.32/0.48      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.32/0.48        = ( ! [X2: A] :
% 0.32/0.48              ( ( P @ X2 )
% 0.32/0.48             => ( Q @ X2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Collect_mono_iff
% 0.32/0.48  thf(fact_134_bot_Oextremum__uniqueI,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order_bot @ A )
% 0.32/0.48       => ! [A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/0.48           => ( A2
% 0.32/0.48              = ( bot_bot @ A ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % bot.extremum_uniqueI
% 0.32/0.48  thf(fact_135_bot_Oextremum__unique,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order_bot @ A )
% 0.32/0.48       => ! [A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/0.48            = ( A2
% 0.32/0.48              = ( bot_bot @ A ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % bot.extremum_unique
% 0.32/0.48  thf(fact_136_bot_Oextremum,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( order_bot @ A )
% 0.32/0.48       => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % bot.extremum
% 0.32/0.48  thf(fact_137_subset__insertI2,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,B2: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_insertI2
% 0.32/0.48  thf(fact_138_subset__insertI,axiom,
% 0.32/0.48      ! [A: $tType,B: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A2 @ B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_insertI
% 0.32/0.48  thf(fact_139_subset__insert,axiom,
% 0.32/0.48      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ~ ( member @ A @ X3 @ A3 )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B ) )
% 0.32/0.48          = ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_insert
% 0.32/0.48  thf(fact_140_insert__mono,axiom,
% 0.32/0.48      ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % insert_mono
% 0.32/0.48  thf(fact_141_pairwise__empty,axiom,
% 0.32/0.48      ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwise_empty
% 0.32/0.48  thf(fact_142_pairwise__insert,axiom,
% 0.32/0.48      ! [A: $tType,R3: A > A > $o,X3: A,S3: set @ A] :
% 0.32/0.48        ( ( pairwise @ A @ R3 @ ( insert @ A @ X3 @ S3 ) )
% 0.32/0.48        = ( ! [Y4: A] :
% 0.32/0.48              ( ( ( member @ A @ Y4 @ S3 )
% 0.32/0.48                & ( Y4 != X3 ) )
% 0.32/0.48             => ( ( R3 @ X3 @ Y4 )
% 0.32/0.48                & ( R3 @ Y4 @ X3 ) ) )
% 0.32/0.48          & ( pairwise @ A @ R3 @ S3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % pairwise_insert
% 0.32/0.48  thf(fact_143_subset__singleton__iff,axiom,
% 0.32/0.48      ! [A: $tType,X5: set @ A,A2: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48        = ( ( X5
% 0.32/0.48            = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48          | ( X5
% 0.32/0.48            = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_singleton_iff
% 0.32/0.48  thf(fact_144_subset__singletonD,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,X3: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48       => ( ( A3
% 0.32/0.48            = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48          | ( A3
% 0.32/0.48            = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_singletonD
% 0.32/0.48  thf(fact_145_TBtheorem2a,axiom,
% 0.32/0.48      ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/0.48        ( ( eout @ PQ @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ( eout @ P @ E )
% 0.32/0.48              | ( eout @ Q @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem2a
% 0.32/0.48  thf(fact_146_TBtheorem5a__notP1,axiom,
% 0.32/0.48      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.48        ( ( eout @ P @ E )
% 0.32/0.48       => ( ~ ( eout @ Q @ E )
% 0.32/0.48         => ( ( ( subcomponents @ PQ )
% 0.32/0.48              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48           => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48             => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                    ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.32/0.48                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.48               => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5a_notP1
% 0.32/0.48  thf(fact_147_TBtheorem5a__notPQ,axiom,
% 0.32/0.48      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.32/0.48        ( ( ( subcomponents @ PQ )
% 0.32/0.48          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48       => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48         => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.32/0.48           => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/0.48             => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/0.48                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48               => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/0.48                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48                 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5a_notPQ
% 0.32/0.48  thf(fact_148_TBtheorem5a__notP2,axiom,
% 0.32/0.48      ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/0.48        ( ~ ( eout @ Q @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.32/0.48             => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/0.48                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48               => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5a_notP2
% 0.32/0.48  thf(fact_149_TBtheorem5a__PQ,axiom,
% 0.32/0.48      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.48        ( ( ( eout @ P @ E )
% 0.32/0.48          | ( eout @ Q @ E ) )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/0.48                    | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.32/0.48                  & ( exprChannel @ Ch2 @ E )
% 0.32/0.48                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.48             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5a_PQ
% 0.32/0.48  thf(fact_150_TBtheorem45a__P,axiom,
% 0.32/0.48      ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/0.48        ( ( eout @ P @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                  ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/0.48                  & ( exprChannel @ Ch2 @ E )
% 0.32/0.48                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.48             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem45a_P
% 0.32/0.48  thf(fact_151_TBtheorem2b,axiom,
% 0.32/0.48      ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/0.48        ( ( eoutM @ PQ @ M @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ( eoutM @ P @ M @ E )
% 0.32/0.48              | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem2b
% 0.32/0.48  thf(fact_152_eoutM__def,axiom,
% 0.32/0.48      ( eoutM
% 0.32/0.48      = ( ^ [SP: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/0.48          ? [Ch3: secrecy_chanID] :
% 0.32/0.48            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/0.48            & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.32/0.48            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % eoutM_def
% 0.32/0.48  thf(fact_153_out__exprChannelSet__def,axiom,
% 0.32/0.48      ( out_exprChannelSet
% 0.32/0.48      = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/0.48            ( ! [X2: secrecy_chanID] :
% 0.32/0.48                ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/0.48               => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.32/0.48                  & ( exprChannel @ X2 @ E2 ) ) )
% 0.32/0.48            & ! [X2: secrecy_chanID] :
% 0.32/0.48                ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/0.48                  & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 0.32/0.48               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % out_exprChannelSet_def
% 0.32/0.48  thf(fact_154_out__exprChannelSingle__def,axiom,
% 0.32/0.48      ( out_ex985543062Single
% 0.32/0.48      = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.32/0.48            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/0.48            & ( exprChannel @ Ch3 @ E2 )
% 0.32/0.48            & ! [X2: secrecy_chanID,T: nat] :
% 0.32/0.48                ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.32/0.48                  & ( X2 != Ch3 ) )
% 0.32/0.48               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % out_exprChannelSingle_def
% 0.32/0.48  thf(fact_155_not__eout__eoutM,axiom,
% 0.32/0.48      ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.32/0.48        ( ~ ( eout @ P @ E )
% 0.32/0.48       => ~ ( eoutM @ P @ M @ E ) ) ).
% 0.32/0.48  
% 0.32/0.48  % not_eout_eoutM
% 0.32/0.48  thf(fact_156_eoutM__eout,axiom,
% 0.32/0.48      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/0.48        ( ( eoutM @ P @ M @ E )
% 0.32/0.48       => ( eout @ P @ E ) ) ).
% 0.32/0.48  
% 0.32/0.48  % eoutM_eout
% 0.32/0.48  thf(fact_157_out__exprChannelSet__Single,axiom,
% 0.32/0.48      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/0.48        ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.32/0.48       => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.32/0.48  
% 0.32/0.48  % out_exprChannelSet_Single
% 0.32/0.48  thf(fact_158_out__exprChannelSingle__Set,axiom,
% 0.32/0.48      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/0.48        ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.32/0.48       => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.32/0.48  
% 0.32/0.48  % out_exprChannelSingle_Set
% 0.32/0.48  thf(fact_159_eout__def,axiom,
% 0.32/0.48      ( eout
% 0.32/0.48      = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.32/0.48          ? [Ch3: secrecy_chanID] :
% 0.32/0.48            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/0.48            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % eout_def
% 0.32/0.48  thf(fact_160_TBtheorem5b__notP2,axiom,
% 0.32/0.48      ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/0.48        ( ~ ( eoutM @ Q @ M @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.32/0.48             => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/0.48                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48               => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5b_notP2
% 0.32/0.48  thf(fact_161_TBtheore54b__P,axiom,
% 0.32/0.48      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/0.48        ( ( eoutM @ P @ M @ E )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                  ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 0.32/0.48                  & ( exprChannel @ Ch2 @ E )
% 0.32/0.48                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.32/0.48                  & ( member @ secrecy_chanID @ Ch2 @ M ) )
% 0.32/0.48             => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheore54b_P
% 0.32/0.48  thf(fact_162_TBtheorem5b__PQ,axiom,
% 0.32/0.48      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.48        ( ( ( eoutM @ P @ M @ E )
% 0.32/0.48          | ( eoutM @ Q @ M @ E ) )
% 0.32/0.48       => ( ( ( subcomponents @ PQ )
% 0.32/0.48            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48         => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48           => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/0.48                    | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.32/0.48                  & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/0.48                  & ( exprChannel @ Ch2 @ E )
% 0.32/0.48                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.48             => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5b_PQ
% 0.32/0.48  thf(fact_163_TBtheorem5b__notP1,axiom,
% 0.32/0.48      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/0.48        ( ( eoutM @ P @ M @ E )
% 0.32/0.48       => ( ~ ( eoutM @ Q @ M @ E )
% 0.32/0.48         => ( ( ( subcomponents @ PQ )
% 0.32/0.48              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48           => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48             => ( ? [Ch2: secrecy_chanID] :
% 0.32/0.48                    ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.32/0.48                    & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/0.48                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/0.48               => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5b_notP1
% 0.32/0.48  thf(fact_164_correctCompositionOut__prop1,axiom,
% 0.32/0.48      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.32/0.48        ( ( ( subcomponents @ PQ )
% 0.32/0.48          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48       => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48         => ( ( member @ secrecy_chanID @ X3 @ ( out @ PQ ) )
% 0.32/0.48           => ( ( member @ secrecy_chanID @ X3 @ ( out @ P ) )
% 0.32/0.48              | ( member @ secrecy_chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % correctCompositionOut_prop1
% 0.32/0.48  thf(fact_165_outStream__def,axiom,
% 0.32/0.48      ( outStream
% 0.32/0.48      = ( ^ [X2: secrecy_specID] :
% 0.32/0.48            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.32/0.48            @ ( out @ X2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % outStream_def
% 0.32/0.48  thf(fact_166_TBtheorem5b__notPQ,axiom,
% 0.32/0.48      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.32/0.48        ( ( ( subcomponents @ PQ )
% 0.32/0.48          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/0.48       => ( ( correc990227761ionOut @ PQ )
% 0.32/0.48         => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.32/0.48           => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/0.48             => ( ( M
% 0.32/0.48                  = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.32/0.48               => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                      ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/0.48                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48                 => ( ! [X4: secrecy_chanID] :
% 0.32/0.48                        ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/0.48                       => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/0.48                   => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % TBtheorem5b_notPQ
% 0.32/0.48  thf(fact_167_insert__subsetI,axiom,
% 0.32/0.48      ! [A: $tType,X3: A,A3: set @ A,X5: set @ A] :
% 0.32/0.48        ( ( member @ A @ X3 @ A3 )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ X5 @ A3 )
% 0.32/0.48         => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X5 ) @ A3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % insert_subsetI
% 0.32/0.48  thf(fact_168_UnCI,axiom,
% 0.32/0.48      ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.32/0.48        ( ( ~ ( member @ A @ C @ B )
% 0.32/0.48         => ( member @ A @ C @ A3 ) )
% 0.32/0.48       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % UnCI
% 0.32/0.48  thf(fact_169_Un__iff,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48        = ( ( member @ A @ C @ A3 )
% 0.32/0.48          | ( member @ A @ C @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_iff
% 0.32/0.48  thf(fact_170_Un__empty,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/0.48          = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48        = ( ( A3
% 0.32/0.48            = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48          & ( B
% 0.32/0.48            = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_empty
% 0.32/0.48  thf(fact_171_Un__insert__left,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,B: set @ A,C4: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/0.48        = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_insert_left
% 0.32/0.48  thf(fact_172_Un__insert__right,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,A2: A,B: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/0.48        = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_insert_right
% 0.32/0.48  thf(fact_173_Un__subset__iff,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.32/0.48        = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/0.48          & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_subset_iff
% 0.32/0.48  thf(fact_174_Un__empty__left,axiom,
% 0.32/0.48      ! [A: $tType,B: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 0.32/0.48        = B ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_empty_left
% 0.32/0.48  thf(fact_175_Un__empty__right,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48        = A3 ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_empty_right
% 0.32/0.48  thf(fact_176_subset__Un__eq,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/0.48        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/0.48              ( ( sup_sup @ ( set @ A ) @ A4 @ B7 )
% 0.32/0.48              = B7 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_Un_eq
% 0.32/0.48  thf(fact_177_subset__UnE,axiom,
% 0.32/0.48      ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48       => ~ ! [A7: set @ A] :
% 0.32/0.48              ( ( ord_less_eq @ ( set @ A ) @ A7 @ A3 )
% 0.32/0.48             => ! [B8: set @ A] :
% 0.32/0.48                  ( ( ord_less_eq @ ( set @ A ) @ B8 @ B )
% 0.32/0.48                 => ( C4
% 0.32/0.48                   != ( sup_sup @ ( set @ A ) @ A7 @ B8 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_UnE
% 0.32/0.48  thf(fact_178_Un__absorb2,axiom,
% 0.32/0.48      ! [A: $tType,B: set @ A,A3: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/0.48       => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/0.48          = A3 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_absorb2
% 0.32/0.48  thf(fact_179_Un__absorb1,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/0.48       => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/0.48          = B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_absorb1
% 0.32/0.48  thf(fact_180_Un__upper2,axiom,
% 0.32/0.48      ! [A: $tType,B: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_upper2
% 0.32/0.48  thf(fact_181_Un__upper1,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_upper1
% 0.32/0.48  thf(fact_182_Un__least,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.32/0.48         => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_least
% 0.32/0.48  thf(fact_183_Un__mono,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/0.48       => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 0.32/0.48         => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_mono
% 0.32/0.48  thf(fact_184_ineM__Un1,axiom,
% 0.32/0.48      ! [P: secrecy_specID,A3: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 0.32/0.48        ( ( ineM @ P @ A3 @ E )
% 0.32/0.48       => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A3 @ B ) @ E ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ineM_Un1
% 0.32/0.48  thf(fact_185_UnE,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48       => ( ~ ( member @ A @ C @ A3 )
% 0.32/0.48         => ( member @ A @ C @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % UnE
% 0.32/0.48  thf(fact_186_UnI1,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ A3 )
% 0.32/0.48       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % UnI1
% 0.32/0.48  thf(fact_187_UnI2,axiom,
% 0.32/0.48      ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ B )
% 0.32/0.48       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % UnI2
% 0.32/0.48  thf(fact_188_bex__Un,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.32/0.48        ( ( ? [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48              & ( P @ X2 ) ) )
% 0.32/0.48        = ( ? [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ A3 )
% 0.32/0.48              & ( P @ X2 ) )
% 0.32/0.48          | ? [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ B )
% 0.32/0.48              & ( P @ X2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % bex_Un
% 0.32/0.48  thf(fact_189_ball__Un,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.32/0.48        ( ( ! [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48             => ( P @ X2 ) ) )
% 0.32/0.48        = ( ! [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ A3 )
% 0.32/0.48             => ( P @ X2 ) )
% 0.32/0.48          & ! [X2: A] :
% 0.32/0.48              ( ( member @ A @ X2 @ B )
% 0.32/0.48             => ( P @ X2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ball_Un
% 0.32/0.48  thf(fact_190_Un__assoc,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.32/0.48        = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_assoc
% 0.32/0.48  thf(fact_191_Un__absorb,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.32/0.48        = A3 ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_absorb
% 0.32/0.48  thf(fact_192_Un__commute,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) )
% 0.32/0.48        = ( ^ [A4: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_commute
% 0.32/0.48  thf(fact_193_Un__left__absorb,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48        = ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_left_absorb
% 0.32/0.48  thf(fact_194_Un__left__commute,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 0.32/0.48        = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_left_commute
% 0.32/0.48  thf(fact_195_singleton__Un__iff,axiom,
% 0.32/0.48      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48          = ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48        = ( ( ( A3
% 0.32/0.48              = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.48          | ( ( A3
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48          | ( ( A3
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % singleton_Un_iff
% 0.32/0.48  thf(fact_196_Un__singleton__iff,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A,X3: A] :
% 0.32/0.48        ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/0.48          = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48        = ( ( ( A3
% 0.32/0.48              = ( bot_bot @ ( set @ A ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.48          | ( ( A3
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48          | ( ( A3
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/0.48            & ( B
% 0.32/0.48              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Un_singleton_iff
% 0.32/0.48  thf(fact_197_insert__is__Un,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( insert @ A )
% 0.32/0.48        = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % insert_is_Un
% 0.32/0.48  thf(fact_198_subset__emptyI,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A] :
% 0.32/0.48        ( ! [X4: A] :
% 0.32/0.48            ~ ( member @ A @ X4 @ A3 )
% 0.32/0.48       => ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_emptyI
% 0.32/0.48  thf(fact_199_sup__bot_Oright__neutral,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [A2: A] :
% 0.32/0.48            ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/0.48            = A2 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot.right_neutral
% 0.32/0.48  thf(fact_200_sup__bot_Oneutr__eq__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [A2: A,B2: A] :
% 0.32/0.48            ( ( ( bot_bot @ A )
% 0.32/0.48              = ( sup_sup @ A @ A2 @ B2 ) )
% 0.32/0.48            = ( ( A2
% 0.32/0.48                = ( bot_bot @ A ) )
% 0.32/0.48              & ( B2
% 0.32/0.48                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot.neutr_eq_iff
% 0.32/0.48  thf(fact_201_sup__bot_Oleft__neutral,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [A2: A] :
% 0.32/0.48            ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.32/0.48            = A2 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot.left_neutral
% 0.32/0.48  thf(fact_202_le__sup__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ ( sup_sup @ A @ X3 @ Y3 ) @ Z2 )
% 0.32/0.48            = ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.32/0.48              & ( ord_less_eq @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_sup_iff
% 0.32/0.48  thf(fact_203_sup_Obounded__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,C: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 0.32/0.48            = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48              & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.bounded_iff
% 0.32/0.48  thf(fact_204_sup__bot__left,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [X3: A] :
% 0.32/0.48            ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 0.32/0.48            = X3 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot_left
% 0.32/0.48  thf(fact_205_sup__bot__right,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [X3: A] :
% 0.32/0.48            ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 0.32/0.48            = X3 ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot_right
% 0.32/0.48  thf(fact_206_bot__eq__sup__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ( bot_bot @ A )
% 0.32/0.48              = ( sup_sup @ A @ X3 @ Y3 ) )
% 0.32/0.48            = ( ( X3
% 0.32/0.48                = ( bot_bot @ A ) )
% 0.32/0.48              & ( Y3
% 0.32/0.48                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % bot_eq_sup_iff
% 0.32/0.48  thf(fact_207_sup__eq__bot__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/0.48              = ( bot_bot @ A ) )
% 0.32/0.48            = ( ( X3
% 0.32/0.48                = ( bot_bot @ A ) )
% 0.32/0.48              & ( Y3
% 0.32/0.48                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_eq_bot_iff
% 0.32/0.48  thf(fact_208_sup__bot_Oeq__neutr__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounde1808546759up_bot @ A )
% 0.32/0.48       => ! [A2: A,B2: A] :
% 0.32/0.48            ( ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/0.48              = ( bot_bot @ A ) )
% 0.32/0.48            = ( ( A2
% 0.32/0.48                = ( bot_bot @ A ) )
% 0.32/0.48              & ( B2
% 0.32/0.48                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_bot.eq_neutr_iff
% 0.32/0.48  thf(fact_209_inf__sup__ord_I4_J,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( lattice @ A )
% 0.32/0.48       => ! [Y3: A,X3: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % inf_sup_ord(4)
% 0.32/0.48  thf(fact_210_inf__sup__ord_I3_J,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( lattice @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % inf_sup_ord(3)
% 0.32/0.48  thf(fact_211_le__supE,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,B2: A,X3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X3 )
% 0.32/0.48           => ~ ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.32/0.48               => ~ ( ord_less_eq @ A @ B2 @ X3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_supE
% 0.32/0.48  thf(fact_212_le__supI,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,X3: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ B2 @ X3 )
% 0.32/0.48             => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_supI
% 0.32/0.48  thf(fact_213_sup__ge1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_ge1
% 0.32/0.48  thf(fact_214_sup__ge2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [Y3: A,X3: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_ge2
% 0.32/0.48  thf(fact_215_le__supI1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [X3: A,A2: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ A2 )
% 0.32/0.48           => ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_supI1
% 0.32/0.48  thf(fact_216_le__supI2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [X3: A,B2: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ B2 )
% 0.32/0.48           => ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_supI2
% 0.32/0.48  thf(fact_217_sup_Omono,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [C: A,A2: A,D: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ D @ B2 )
% 0.32/0.48             => ( ord_less_eq @ A @ ( sup_sup @ A @ C @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.mono
% 0.32/0.48  thf(fact_218_sup__mono,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,C: A,B2: A,D: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ C )
% 0.32/0.48           => ( ( ord_less_eq @ A @ B2 @ D )
% 0.32/0.48             => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C @ D ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_mono
% 0.32/0.48  thf(fact_219_sup__least,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [Y3: A,X3: A,Z2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.32/0.48             => ( ord_less_eq @ A @ ( sup_sup @ A @ Y3 @ Z2 ) @ X3 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_least
% 0.32/0.48  thf(fact_220_le__iff__sup,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ( ( ord_less_eq @ A )
% 0.32/0.48          = ( ^ [X2: A,Y4: A] :
% 0.32/0.48                ( ( sup_sup @ A @ X2 @ Y4 )
% 0.32/0.48                = Y4 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_iff_sup
% 0.32/0.48  thf(fact_221_sup_OorderE,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48           => ( A2
% 0.32/0.48              = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.orderE
% 0.32/0.48  thf(fact_222_sup_OorderI,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,B2: A] :
% 0.32/0.48            ( ( A2
% 0.32/0.48              = ( sup_sup @ A @ A2 @ B2 ) )
% 0.32/0.48           => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.orderI
% 0.32/0.48  thf(fact_223_sup__unique,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [F: A > A > A,X3: A,Y3: A] :
% 0.32/0.48            ( ! [X4: A,Y2: A] : ( ord_less_eq @ A @ X4 @ ( F @ X4 @ Y2 ) )
% 0.32/0.48           => ( ! [X4: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X4 @ Y2 ) )
% 0.32/0.48             => ( ! [X4: A,Y2: A,Z3: A] :
% 0.32/0.48                    ( ( ord_less_eq @ A @ Y2 @ X4 )
% 0.32/0.48                   => ( ( ord_less_eq @ A @ Z3 @ X4 )
% 0.32/0.48                     => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X4 ) ) )
% 0.32/0.48               => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/0.48                  = ( F @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_unique
% 0.32/0.48  thf(fact_224_sup_Oabsorb1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48           => ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/0.48              = A2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.absorb1
% 0.32/0.48  thf(fact_225_sup_Oabsorb2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48           => ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/0.48              = B2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.absorb2
% 0.32/0.48  thf(fact_226_sup__absorb1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [Y3: A,X3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/0.48           => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/0.48              = X3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_absorb1
% 0.32/0.48  thf(fact_227_sup__absorb2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48           => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/0.48              = Y3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup_absorb2
% 0.32/0.48  thf(fact_228_sup_OboundedE,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,C: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 0.32/0.48           => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48               => ~ ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.boundedE
% 0.32/0.48  thf(fact_229_sup_OboundedI,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,A2: A,C: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48           => ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/0.48             => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.boundedI
% 0.32/0.48  thf(fact_230_sup_Oorder__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ( ( ord_less_eq @ A )
% 0.32/0.48          = ( ^ [B5: A,A5: A] :
% 0.32/0.48                ( A5
% 0.32/0.48                = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.order_iff
% 0.32/0.48  thf(fact_231_sup_Ocobounded1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.cobounded1
% 0.32/0.48  thf(fact_232_sup_Ocobounded2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.cobounded2
% 0.32/0.48  thf(fact_233_sup_Oabsorb__iff1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ( ( ord_less_eq @ A )
% 0.32/0.48          = ( ^ [B5: A,A5: A] :
% 0.32/0.48                ( ( sup_sup @ A @ A5 @ B5 )
% 0.32/0.48                = A5 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.absorb_iff1
% 0.32/0.48  thf(fact_234_sup_Oabsorb__iff2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ( ( ord_less_eq @ A )
% 0.32/0.48          = ( ^ [A5: A,B5: A] :
% 0.32/0.48                ( ( sup_sup @ A @ A5 @ B5 )
% 0.32/0.48                = B5 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.absorb_iff2
% 0.32/0.48  thf(fact_235_sup_OcoboundedI1,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [C: A,A2: A,B2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/0.48           => ( ord_less_eq @ A @ C @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.coboundedI1
% 0.32/0.48  thf(fact_236_sup_OcoboundedI2,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A )
% 0.32/0.48       => ! [C: A,B2: A,A2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ C @ B2 )
% 0.32/0.48           => ( ord_less_eq @ A @ C @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % sup.coboundedI2
% 0.32/0.48  thf(fact_237_correctInOutLoc__def,axiom,
% 0.32/0.48      ( correctInOutLoc
% 0.32/0.48      = ( ^ [X2: secrecy_specID] :
% 0.32/0.48            ( ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( ins @ X2 ) @ ( out @ X2 ) )
% 0.32/0.48              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/0.48            & ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( ins @ X2 ) @ ( loc @ X2 ) )
% 0.32/0.48              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/0.48            & ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( loc @ X2 ) @ ( out @ X2 ) )
% 0.32/0.48              = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % correctInOutLoc_def
% 0.32/0.48  thf(fact_238_subset__Compl__singleton,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B2: A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/0.48        = ( ~ ( member @ A @ B2 @ A3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % subset_Compl_singleton
% 0.32/0.48  thf(fact_239_IntI,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ A3 )
% 0.32/0.48       => ( ( member @ A @ C @ B )
% 0.32/0.48         => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % IntI
% 0.32/0.48  thf(fact_240_Int__iff,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48        = ( ( member @ A @ C @ A3 )
% 0.32/0.48          & ( member @ A @ C @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_iff
% 0.32/0.48  thf(fact_241_ComplI,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A] :
% 0.32/0.48        ( ~ ( member @ A @ C @ A3 )
% 0.32/0.48       => ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % ComplI
% 0.32/0.48  thf(fact_242_Compl__iff,axiom,
% 0.32/0.48      ! [A: $tType,C: A,A3: set @ A] :
% 0.32/0.48        ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.32/0.48        = ( ~ ( member @ A @ C @ A3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Compl_iff
% 0.32/0.48  thf(fact_243_Compl__eq__Compl__iff,axiom,
% 0.32/0.48      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 0.32/0.48          = ( uminus_uminus @ ( set @ A ) @ B ) )
% 0.32/0.48        = ( A3 = B ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Compl_eq_Compl_iff
% 0.32/0.48  thf(fact_244_compl__le__compl__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( boolean_algebra @ A )
% 0.32/0.48       => ! [X3: A,Y3: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y3 ) )
% 0.32/0.48            = ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % compl_le_compl_iff
% 0.32/0.48  thf(fact_245_le__inf__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_inf @ A )
% 0.32/0.48       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.32/0.48            = ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48              & ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % le_inf_iff
% 0.32/0.48  thf(fact_246_inf_Obounded__iff,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( semilattice_inf @ A )
% 0.32/0.48       => ! [A2: A,B2: A,C: A] :
% 0.32/0.48            ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.32/0.48            = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48              & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % inf.bounded_iff
% 0.32/0.48  thf(fact_247_inf__bot__left,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounded_lattice_bot @ A )
% 0.32/0.48       => ! [X3: A] :
% 0.32/0.48            ( ( inf_inf @ A @ ( bot_bot @ A ) @ X3 )
% 0.32/0.48            = ( bot_bot @ A ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % inf_bot_left
% 0.32/0.48  thf(fact_248_inf__bot__right,axiom,
% 0.32/0.48      ! [A: $tType] :
% 0.32/0.48        ( ( bounded_lattice_bot @ A )
% 0.32/0.48       => ! [X3: A] :
% 0.32/0.48            ( ( inf_inf @ A @ X3 @ ( bot_bot @ A ) )
% 0.32/0.48            = ( bot_bot @ A ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % inf_bot_right
% 0.32/0.48  thf(fact_249_Int__insert__left__if0,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,C4: set @ A,B: set @ A] :
% 0.32/0.48        ( ~ ( member @ A @ A2 @ C4 )
% 0.32/0.48       => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/0.48          = ( inf_inf @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_insert_left_if0
% 0.32/0.48  thf(fact_250_Int__insert__left__if1,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,C4: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ A2 @ C4 )
% 0.32/0.48       => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/0.48          = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B @ C4 ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_insert_left_if1
% 0.32/0.48  thf(fact_251_insert__inter__insert,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ ( insert @ A @ A2 @ B ) )
% 0.32/0.48        = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % insert_inter_insert
% 0.32/0.48  thf(fact_252_Int__insert__right__if0,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ~ ( member @ A @ A2 @ A3 )
% 0.32/0.48       => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/0.48          = ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_insert_right_if0
% 0.32/0.48  thf(fact_253_Int__insert__right__if1,axiom,
% 0.32/0.48      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( member @ A @ A2 @ A3 )
% 0.32/0.48       => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/0.48          = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_insert_right_if1
% 0.32/0.48  thf(fact_254_Int__subset__iff,axiom,
% 0.32/0.48      ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 0.32/0.48        ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) )
% 0.32/0.48        = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 0.32/0.48          & ( ord_less_eq @ ( set @ A ) @ C4 @ B ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_subset_iff
% 0.32/0.48  thf(fact_255_Int__Un__eq_I4_J,axiom,
% 0.32/0.48      ! [A: $tType,T2: set @ A,S: set @ A] :
% 0.32/0.48        ( ( sup_sup @ ( set @ A ) @ T2 @ ( inf_inf @ ( set @ A ) @ S @ T2 ) )
% 0.32/0.48        = T2 ) ).
% 0.32/0.48  
% 0.32/0.48  % Int_Un_eq(4)
% 0.32/0.48  
% 0.32/0.48  % Type constructors (46)
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.32/0.48      bounded_lattice @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.32/0.48      ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( bounded_lattice @ A9 )
% 0.32/0.48       => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( bounded_lattice @ A9 )
% 0.32/0.48       => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( bounded_lattice @ A9 )
% 0.32/0.48       => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( semilattice_sup @ A9 )
% 0.32/0.48       => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( semilattice_inf @ A9 )
% 0.32/0.48       => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( boolean_algebra @ A9 )
% 0.32/0.48       => ( boolean_algebra @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( order_bot @ A9 )
% 0.32/0.48       => ( order_bot @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( preorder @ A9 )
% 0.32/0.48       => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Lattices_Olattice,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( lattice @ A9 )
% 0.32/0.48       => ( lattice @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( order @ A9 )
% 0.32/0.48       => ( order @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( ord @ A9 )
% 0.32/0.48       => ( ord @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_fun___Orderings_Obot,axiom,
% 0.32/0.48      ! [A8: $tType,A9: $tType] :
% 0.32/0.48        ( ( bot @ A9 )
% 0.32/0.48       => ( bot @ ( A8 > A9 ) ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.32/0.48      semilattice_sup @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4,axiom,
% 0.32/0.48      semilattice_inf @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Oorder__bot_5,axiom,
% 0.32/0.48      order_bot @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Opreorder_6,axiom,
% 0.32/0.48      preorder @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/0.48      linorder @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Lattices_Olattice_7,axiom,
% 0.32/0.48      lattice @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Oorder_8,axiom,
% 0.32/0.48      order @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Oord_9,axiom,
% 0.32/0.48      ord @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Nat_Onat___Orderings_Obot_10,axiom,
% 0.32/0.48      bot @ nat ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_11,axiom,
% 0.32/0.48      ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_12,axiom,
% 0.32/0.48      ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Osemilattice__sup_13,axiom,
% 0.32/0.48      ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Osemilattice__inf_14,axiom,
% 0.32/0.48      ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Oboolean__algebra_15,axiom,
% 0.32/0.48      ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Orderings_Oorder__bot_16,axiom,
% 0.32/0.48      ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Orderings_Opreorder_17,axiom,
% 0.32/0.48      ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Lattices_Olattice_18,axiom,
% 0.32/0.48      ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Orderings_Oorder_19,axiom,
% 0.32/0.48      ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Orderings_Oord_20,axiom,
% 0.32/0.48      ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_Set_Oset___Orderings_Obot_21,axiom,
% 0.32/0.48      ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_22,axiom,
% 0.32/0.48      bounde1808546759up_bot @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_23,axiom,
% 0.32/0.48      bounded_lattice_bot @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_24,axiom,
% 0.32/0.48      semilattice_sup @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_25,axiom,
% 0.32/0.48      semilattice_inf @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_26,axiom,
% 0.32/0.48      boolean_algebra @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Oorder__bot_27,axiom,
% 0.32/0.48      order_bot @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Opreorder_28,axiom,
% 0.32/0.48      preorder @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Olinorder_29,axiom,
% 0.32/0.48      linorder @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Lattices_Olattice_30,axiom,
% 0.32/0.48      lattice @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Oorder_31,axiom,
% 0.32/0.48      order @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Oord_32,axiom,
% 0.32/0.48      ord @ $o ).
% 0.32/0.48  
% 0.32/0.48  thf(tcon_HOL_Obool___Orderings_Obot_33,axiom,
% 0.32/0.48      bot @ $o ).
% 0.32/0.48  
% 0.32/0.48  % Conjectures (1)
% 0.32/0.48  thf(conj_0,conjecture,
% 0.32/0.48      member @ secrecy_chanID @ ch @ ( loc @ pq ) ).
% 0.32/0.48  
% 0.32/0.48  %------------------------------------------------------------------------------
% 0.32/0.48  ------------------------
% 2.57/1.60  ---- Embedded in THF ---
% 0.32/1.60  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.60  %%% Generated on Tue Feb 24 08:24:27 EST 2026
% 0.32/1.60  %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.60  %%% Logic specification used:
% 0.32/1.60  %%% thf(spec, logic, $$dhol).
% 0.32/1.60  
% 0.32/1.60  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2DTF7835.p
% 0.32/1.60  thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 0.32/1.60  thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 0.32/1.60  thf(ty_t_Secrecy__types_OchanID, type, secrecy_chanID: $tType).
% 0.32/1.60  thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.32/1.60  thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.32/1.60  thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 0.32/1.60  thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.32/1.60  thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 0.32/1.60  thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 0.32/1.60  thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 0.32/1.60  thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.32/1.60  thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 0.32/1.60  thf(sy_c_Secrecy_OeoutM, type, eoutM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Secrecy_OexprChannel, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))).
% 0.32/1.60  thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 0.32/1.60  thf(sy_c_Secrecy_OineM, type, ineM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Secrecy_Oine__exprChannelSet, type, ine_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Secrecy_Oine__exprChannelSingle, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Secrecy_Oout__exprChannelSet, type, out_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Secrecy_Oout__exprChannelSingle, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 0.32/1.60  thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.32/1.60  thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 0.32/1.60  thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.32/1.60  thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.32/1.60  thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 0.32/1.60  thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 0.32/1.60  thf(sy_c_inout_OcorrectCompositionIn, type, correctCompositionIn: (secrecy_specID > $o)).
% 0.32/1.60  thf(sy_c_inout_OcorrectCompositionLoc, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 0.32/1.60  thf(sy_c_inout_OcorrectCompositionOut, type, correc990227761ionOut: (secrecy_specID > $o)).
% 0.32/1.60  thf(sy_c_inout_OcorrectInOutLoc, type, correctInOutLoc: (secrecy_specID > $o)).
% 0.32/1.60  thf(sy_c_inout_OinStream, type, inStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 0.32/1.60  thf(sy_c_inout_Oins, type, ins: (secrecy_specID > (set @ secrecy_chanID))).
% 0.32/1.60  thf(sy_c_inout_Oloc, type, loc: (secrecy_specID > (set @ secrecy_chanID))).
% 0.32/1.60  thf(sy_c_inout_OlocStream, type, locStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 0.32/1.60  thf(sy_c_inout_Oout, type, out: (secrecy_specID > (set @ secrecy_chanID))).
% 0.32/1.60  thf(sy_c_inout_OoutStream, type, outStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 0.32/1.60  thf(sy_c_inout_Osubcomponents, type, subcomponents: (secrecy_specID > (set @ secrecy_specID))).
% 0.32/1.60  thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.32/1.60  thf(sy_v_P, type, p: secrecy_specID).
% 0.32/1.60  thf(sy_v_PQ, type, pq: secrecy_specID).
% 0.32/1.60  thf(sy_v_Q, type, q: secrecy_specID).
% 0.32/1.60  thf(sy_v_ch, type, ch: secrecy_chanID).
% 0.32/1.60  thf(sy_v_m, type, m: secrecy_Expression).
% 0.32/1.60  thf(fact_0_assms_I2_J, axiom, (correctCompositionIn @ pq)).
% 0.32/1.60  thf(fact_1_assms_I4_J, axiom, ((exprChannel @ ch) @ m)).
% 0.32/1.60  thf(fact_2_assms_I3_J, axiom, (((member @ secrecy_chanID) @ ch) @ (ins @ p))).
% 0.32/1.60  thf(fact_3_assms_I5_J, axiom, (! [X:secrecy_chanID]: (((((member @ secrecy_chanID) @ X) @ (ins @ pq)) => (~ (((exprChannel @ X) @ m))))))).
% 0.32/1.60  thf(fact_4_assms_I1_J, axiom, ((subcomponents @ pq) = (((insert @ secrecy_specID) @ p) @ (((insert @ secrecy_specID) @ q) @ (bot_bot @ (set @ secrecy_specID)))))).
% 0.32/1.60  thf(fact_5_locStream__def, axiom, (locStream = (^ [X2:secrecy_specID]: (((^ [Y:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y = Z))) @ (loc @ X2)))))).
% 0.32/1.60  thf(fact_6_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))))))))).
% 0.32/1.60  thf(fact_7_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))))))))).
% 0.32/1.60  thf(fact_8_correctCompositionIn__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X3:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ X3) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ X3) @ (ins @ P)) | (((member @ secrecy_chanID) @ X3) @ (ins @ Q))))))))).
% 0.32/1.60  thf(fact_9_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_10_TBtheorem4b__P, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((ineM @ P) @ M) @ 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) @ M)))))) => (((ineM @ PQ) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_11_TBtheorem4b__PQ, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((ineM @ P) @ M) @ E) | (((ineM @ Q) @ M) @ 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) @ M) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((ineM @ PQ) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_12_TBlemma3b, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((ineM @ P) @ M) @ E))) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ M) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => (~ (((exprChannel @ Ch) @ E)))))))))))).
% 0.32/1.60  thf(fact_13_inStream__def, axiom, (inStream = (^ [X2:secrecy_specID]: (((^ [Y:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y = Z))) @ (ins @ X2)))))).
% 0.32/1.60  thf(fact_14_insertCI, axiom, (! [A:$tType,A2:A,B:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B)))))).
% 0.32/1.60  thf(fact_15_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A3)) = ((A2 = B2) | (((member @ A) @ A2) @ A3)))))).
% 0.32/1.60  thf(fact_16_insert__absorb2, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A3)) = (((insert @ A) @ X3) @ A3))))).
% 0.32/1.60  thf(fact_17_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 0.32/1.60  thf(fact_18_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_19_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 0.32/1.60  thf(fact_20_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 0.32/1.60  thf(fact_21_ineM__def, axiom, (ineM = (^ [SP:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & ((exprChannel @ Ch3) @ E2))))))))).
% 0.32/1.60  thf(fact_22_ineM__L1, axiom, (! [Ch:secrecy_chanID,M:(set @ secrecy_chanID),P:secrecy_specID,E:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch) @ M) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ E) => (((ineM @ P) @ M) @ E))))))).
% 0.32/1.60  thf(fact_23_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_24_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_25_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 0.32/1.60  thf(fact_26_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 0.32/1.60  thf(fact_27_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B3:(set @ A)]: (((A3 = (((insert @ A) @ A2) @ B3)) & (~ ((((member @ A) @ A2) @ B3)))))))))).
% 0.32/1.60  thf(fact_28_insert__commute, axiom, (! [A:$tType,X3:A,Y3:A,A3:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y3) @ A3)) = (((insert @ A) @ Y3) @ (((insert @ A) @ X3) @ A3)))))).
% 0.32/1.60  thf(fact_29_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B2:A,B:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B2) @ B))) => (((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B2) @ B)) = (((A2 = B2) => (A3 = B)) & ((A2 != B2) => (? [C2:(set @ A)]: (((A3 = (((insert @ A) @ B2) @ C2)) & ((~ ((((member @ A) @ B2) @ C2))) & ((B = (((insert @ A) @ A2) @ C2)) & (~ ((((member @ A) @ A2) @ C2)))))))))))))))).
% 0.32/1.60  thf(fact_30_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert @ A) @ A2) @ A3) = A3))))).
% 0.32/1.60  thf(fact_31_insert__ident, axiom, (! [A:$tType,X3:A,A3:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((~ ((((member @ A) @ X3) @ B))) => (((((insert @ A) @ X3) @ A3) = (((insert @ A) @ X3) @ B)) = (A3 = B))))))).
% 0.32/1.60  thf(fact_32_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((member @ A) @ X3) @ A3) => (~ ((! [B3:(set @ A)]: (((A3 = (((insert @ A) @ X3) @ B3)) => (((member @ A) @ X3) @ B3)))))))))).
% 0.32/1.60  thf(fact_33_insertI2, axiom, (! [A:$tType,A2:A,B:(set @ A),B2:A]: (((((member @ A) @ A2) @ B) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B)))))).
% 0.32/1.60  thf(fact_34_insertI1, axiom, (! [A:$tType,A2:A,B:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B))))).
% 0.32/1.60  thf(fact_35_insertE, axiom, (! [A:$tType,A2:A,B2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A3)) => ((A2 != B2) => (((member @ A) @ A2) @ A3)))))).
% 0.32/1.60  thf(fact_36_TBtheorem3b, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((ineM @ P) @ M) @ E))) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ ((((ineM @ PQ) @ M) @ E)))))))))).
% 0.32/1.60  thf(fact_37_TBtheorem1b, axiom, (! [PQ:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((ineM @ PQ) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ineM @ P) @ M) @ E) | (((ineM @ Q) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_38_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 0.32/1.60  thf(fact_39_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 0.32/1.60  thf(fact_40_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C:A,D:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A2 = C) & (B2 = D)) | ((A2 = D) & (B2 = C))))))).
% 0.32/1.60  thf(fact_41_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 0.32/1.60  thf(fact_42_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 0.32/1.60  thf(fact_43_TBtheorem4b__notP1, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ineM @ P) @ M) @ E) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch2) @ E) & ((((member @ secrecy_chanID) @ Ch2) @ M) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((ineM @ PQ) @ M) @ E))))))))))).
% 0.32/1.60  thf(fact_44_TBtheorem4b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetP) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetQ) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M) @ E)))))))))))).
% 0.32/1.60  thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.32/1.60  thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 0.32/1.60  thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.32/1.60  thf(fact_48_ext, axiom, (! [B4:$tType,A:$tType,F:(A > B4),G:(A > B4)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 0.32/1.60  thf(fact_49_TBtheorem4b__notP2, axiom, (! [Q:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSet) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M) @ E))))))))))).
% 0.32/1.60  thf(fact_50_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 0.32/1.60  thf(fact_51_bot__apply, axiom, (! [C3:$tType,D2:$tType]: (((bot @ C3) => ((bot_bot @ (D2 > C3)) = (^ [X2:D2]: ((bot_bot @ C3)))))))).
% 0.32/1.60  thf(fact_52_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)))))))).
% 0.32/1.60  thf(fact_53_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)))))))).
% 0.32/1.60  thf(fact_54_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_55_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)))))))).
% 0.32/1.60  thf(fact_56_ine__exprChannelSingle__def, axiom, (ine_ex1303305700Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & (((exprChannel @ Ch3) @ E2) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & (X2 != Ch3)) => (~ (((exprChannel @ X2) @ E2)))))))))))).
% 0.32/1.60  thf(fact_57_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)))))))).
% 0.32/1.60  thf(fact_58_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))))).
% 0.32/1.60  thf(fact_59_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))))).
% 0.32/1.60  thf(fact_60_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)))))).
% 0.32/1.60  thf(fact_61_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 0.32/1.60  thf(fact_62_not__ine__ineM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M:(set @ secrecy_chanID)]: (((~ (((ine @ P) @ E))) => (~ ((((ineM @ P) @ M) @ E))))))).
% 0.32/1.60  thf(fact_63_ineM__ine, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ineM @ P) @ M) @ E) => ((ine @ P) @ E))))).
% 0.32/1.60  thf(fact_64_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 0.32/1.60  thf(fact_65_ine__def, axiom, (ine = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((exprChannel @ Ch3) @ E2)))))))).
% 0.32/1.60  thf(fact_66_ine__ins__neg1, axiom, (! [P:secrecy_specID,M3:secrecy_Expression,X3:secrecy_chanID]: (((~ (((ine @ P) @ M3))) => (((exprChannel @ X3) @ M3) => (~ ((((member @ secrecy_chanID) @ X3) @ (ins @ P))))))))).
% 0.32/1.60  thf(fact_67_is__singletonI_H, axiom, (! [A:$tType,A3:(set @ A)]: (((A3 != (bot_bot @ (set @ A))) => ((! [X4:A,Y2:A]: (((((member @ A) @ X4) @ A3) => ((((member @ A) @ Y2) @ A3) => (X4 = Y2))))) => ((is_singleton @ A) @ A3)))))).
% 0.32/1.60  thf(fact_68_bot__fun__def, axiom, (! [B4:$tType,A:$tType]: (((bot @ B4) => ((bot_bot @ (A > B4)) = (^ [X2:A]: ((bot_bot @ B4)))))))).
% 0.32/1.60  thf(fact_69_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))))))))))).
% 0.32/1.60  thf(fact_70_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)))))))))))).
% 0.32/1.60  thf(fact_71_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))))))))))).
% 0.32/1.60  thf(fact_72_ine__exprChannelSet__def, axiom, (ine_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & ((exprChannel @ X2) @ E2))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (ins @ SP))) => (~ (((exprChannel @ X2) @ E2))))))))))).
% 0.32/1.60  thf(fact_73_is__singletonE, axiom, (! [A:$tType,A3:(set @ A)]: ((((is_singleton @ A) @ A3) => (~ ((! [X4:A]: ((A3 != (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 0.32/1.60  thf(fact_74_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X2:A]: ((A4 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 0.32/1.60  thf(fact_75_TBtheorem1a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((ine @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((ine @ P) @ E) | ((ine @ Q) @ E)))))))).
% 0.32/1.60  thf(fact_76_TBtheorem3a, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((ine @ P) @ E))) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ E)))))))))).
% 0.32/1.60  thf(fact_77_subcomponents__loc, axiom, (! [X3:secrecy_specID]: (((correc965049635ionLoc @ X3) => (((subcomponents @ X3) = (bot_bot @ (set @ secrecy_specID))) => ((loc @ X3) = (bot_bot @ (set @ secrecy_chanID)))))))).
% 0.32/1.60  thf(fact_78_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_79_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)))))))).
% 0.32/1.60  thf(fact_80_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_81_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 0.32/1.60  thf(fact_82_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A3:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_83_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A3:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A3)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_84_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 0.32/1.60  thf(fact_85_subsetI, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A3) => (((member @ A) @ X4) @ B)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B))))).
% 0.32/1.60  thf(fact_86_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ A3) => (A3 = B)))))).
% 0.32/1.60  thf(fact_87_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 0.32/1.60  thf(fact_88_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_89_insert__subset, axiom, (! [A:$tType,X3:A,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A3)) @ B) = ((((member @ A) @ X3) @ B) & (((ord_less_eq @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_90_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A3:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_91_le__funD, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4),X3:A]: (((((ord_less_eq @ (A > B4)) @ F) @ G) => (((ord_less_eq @ B4) @ (F @ X3)) @ (G @ X3))))))))).
% 0.32/1.60  thf(fact_92_le__funE, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4),X3:A]: (((((ord_less_eq @ (A > B4)) @ F) @ G) => (((ord_less_eq @ B4) @ (F @ X3)) @ (G @ X3))))))))).
% 0.32/1.60  thf(fact_93_le__funI, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4)]: (((! [X4:A]: ((((ord_less_eq @ B4) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B4)) @ F) @ G)))))))).
% 0.32/1.60  thf(fact_94_le__fun__def, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => ((ord_less_eq @ (A > B4)) = (^ [F2:(A > B4),G2:(A > B4)]: ((! [X2:A]: ((((ord_less_eq @ B4) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 0.32/1.60  thf(fact_95_order__subst1, axiom, (! [A:$tType,B4:$tType]: ((((order @ B4) & (order @ A)) => (! [A2:A,F:(B4 > A),B2:B4,C:B4]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B4) @ B2) @ C) => ((! [X4:B4,Y2:B4]: (((((ord_less_eq @ B4) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.32/1.60  thf(fact_96_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F @ B2)) @ C) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ C3) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ C3) @ (F @ A2)) @ C)))))))))).
% 0.32/1.60  thf(fact_97_ord__eq__le__subst, axiom, (! [A:$tType,B4:$tType]: ((((ord @ B4) & (ord @ A)) => (! [A2:A,F:(B4 > A),B2:B4,C:B4]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B4) @ B2) @ C) => ((! [X4:B4,Y2:B4]: (((((ord_less_eq @ B4) @ X4) @ Y2) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.32/1.60  thf(fact_98_ord__le__eq__subst, axiom, (! [A:$tType,B4:$tType]: ((((ord @ B4) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B4),C:B4]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X4:A,Y2:A]: (((((ord_less_eq @ A) @ X4) @ Y2) => (((ord_less_eq @ B4) @ (F @ X4)) @ (F @ Y2))))) => (((ord_less_eq @ B4) @ (F @ A2)) @ C)))))))))).
% 0.32/1.60  thf(fact_99_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X2))))))))).
% 0.32/1.60  thf(fact_100_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X3) => (X3 = Y3))))))))).
% 0.32/1.60  thf(fact_101_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 0.32/1.60  thf(fact_102_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((X3 = Y3) => (((ord_less_eq @ A) @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_103_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 0.32/1.60  thf(fact_104_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.60  thf(fact_105_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X3)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y3))))))))))))))))).
% 0.32/1.60  thf(fact_106_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y3) = (X3 = Y3))))))))).
% 0.32/1.60  thf(fact_107_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) & (((ord_less_eq @ A) @ B5) @ A5))))))))).
% 0.32/1.60  thf(fact_108_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.60  thf(fact_109_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.60  thf(fact_110_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 0.32/1.60  thf(fact_111_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 0.32/1.60  thf(fact_112_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.32/1.60  thf(fact_113_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_114_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 0.32/1.60  thf(fact_115_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y:A,Z:A]: ((Y = Z))) = (^ [A5:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A5) & (((ord_less_eq @ A) @ A5) @ B5))))))))).
% 0.32/1.60  thf(fact_116_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 0.32/1.60  thf(fact_117_in__mono, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B)))))).
% 0.32/1.60  thf(fact_118_subsetD, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ B)))))).
% 0.32/1.60  thf(fact_119_equalityE, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B) => (~ ((((ord_less_eq @ (set @ A)) @ B) @ A3)))))))))).
% 0.32/1.60  thf(fact_120_pairwiseD, axiom, (! [A:$tType,R:(A > (A > $o)),S:(set @ A),X3:A,Y3:A]: (((((pairwise @ A) @ R) @ S) => ((((member @ A) @ X3) @ S) => ((((member @ A) @ Y3) @ S) => ((X3 != Y3) => ((R @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_121_pairwiseI, axiom, (! [A:$tType,S:(set @ A),R:(A > (A > $o))]: (((! [X4:A,Y2:A]: (((((member @ A) @ X4) @ S) => ((((member @ A) @ Y2) @ S) => ((X4 != Y2) => ((R @ X4) @ Y2)))))) => (((pairwise @ A) @ R) @ S))))).
% 0.32/1.60  thf(fact_122_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B7:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B7)))))))))).
% 0.32/1.60  thf(fact_123_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (((ord_less_eq @ (set @ A)) @ A3) @ B))))).
% 0.32/1.60  thf(fact_124_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (((ord_less_eq @ (set @ A)) @ B) @ A3))))).
% 0.32/1.60  thf(fact_125_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B7:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A4) => (((member @ A) @ T) @ B7)))))))))).
% 0.32/1.60  thf(fact_126_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 0.32/1.60  thf(fact_127_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.32/1.60  thf(fact_128_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R2:(A > (A > $o)),S2:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ S2) => (! [Y4:A]: (((((member @ A) @ Y4) @ S2) => ((X2 != Y4) => ((R2 @ X2) @ Y4)))))))))))))).
% 0.32/1.60  thf(fact_129_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 0.32/1.60  thf(fact_130_pairwise__mono, axiom, (! [A:$tType,P:(A > (A > $o)),A3:(set @ A),Q:(A > (A > $o)),B:(set @ A)]: (((((pairwise @ A) @ P) @ A3) => ((! [X4:A,Y2:A]: ((((P @ X4) @ Y2) => ((Q @ X4) @ Y2)))) => ((((ord_less_eq @ (set @ A)) @ B) @ A3) => (((pairwise @ A) @ Q) @ B))))))).
% 0.32/1.60  thf(fact_131_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y:(set @ A),Z:(set @ A)]: ((Y = Z))) = (^ [A4:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A4)))))))).
% 0.32/1.60  thf(fact_132_pairwise__subset, axiom, (! [A:$tType,P:(A > (A > $o)),S:(set @ A),T2:(set @ A)]: (((((pairwise @ A) @ P) @ S) => ((((ord_less_eq @ (set @ A)) @ T2) @ S) => (((pairwise @ A) @ P) @ T2)))))).
% 0.32/1.60  thf(fact_133_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 0.32/1.60  thf(fact_134_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 0.32/1.60  thf(fact_135_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 0.32/1.60  thf(fact_136_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 0.32/1.60  thf(fact_137_subset__insertI2, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 0.32/1.60  thf(fact_138_subset__insertI, axiom, (! [A:$tType,B:(set @ A),A2:A]: ((((ord_less_eq @ (set @ A)) @ B) @ (((insert @ A) @ A2) @ B))))).
% 0.32/1.60  thf(fact_139_subset__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X3) @ B)) = (((ord_less_eq @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_140_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A2) @ C4)) @ (((insert @ A) @ A2) @ D3)))))).
% 0.32/1.60  thf(fact_141_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 0.32/1.60  thf(fact_142_pairwise__insert, axiom, (! [A:$tType,R3:(A > (A > $o)),X3:A,S3:(set @ A)]: (((((pairwise @ A) @ R3) @ (((insert @ A) @ X3) @ S3)) = ((! [Y4:A]: ((((((member @ A) @ Y4) @ S3) & (Y4 != X3)) => (((R3 @ X3) @ Y4) & ((R3 @ Y4) @ X3))))) & (((pairwise @ A) @ R3) @ S3)))))).
% 0.32/1.60  thf(fact_143_subset__singleton__iff, axiom, (! [A:$tType,X5:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ X5) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = ((X5 = (bot_bot @ (set @ A))) | (X5 = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_144_subset__singletonD, axiom, (! [A:$tType,A3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) => ((A3 = (bot_bot @ (set @ A))) | (A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))).
% 0.32/1.60  thf(fact_145_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)))))))).
% 0.32/1.60  thf(fact_146_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))))))))))).
% 0.32/1.60  thf(fact_147_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)))))))))))).
% 0.32/1.60  thf(fact_148_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))))))))))).
% 0.32/1.60  thf(fact_149_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)))))))).
% 0.32/1.60  thf(fact_150_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)))))))).
% 0.32/1.60  thf(fact_151_TBtheorem2b, axiom, (! [PQ:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ PQ) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((eoutM @ P) @ M) @ E) | (((eoutM @ Q) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_152_eoutM__def, axiom, (eoutM = (^ [SP:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & ((exprChannel @ Ch3) @ E2))))))))).
% 0.32/1.60  thf(fact_153_out__exprChannelSet__def, axiom, (out_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & ((exprChannel @ X2) @ E2))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (out @ SP))) => (~ (((exprChannel @ X2) @ E2))))))))))).
% 0.32/1.60  thf(fact_154_out__exprChannelSingle__def, axiom, (out_ex985543062Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & (((exprChannel @ Ch3) @ E2) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & (X2 != Ch3)) => (~ (((exprChannel @ X2) @ E2)))))))))))).
% 0.32/1.60  thf(fact_155_not__eout__eoutM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M:(set @ secrecy_chanID)]: (((~ (((eout @ P) @ E))) => (~ ((((eoutM @ P) @ M) @ E))))))).
% 0.32/1.60  thf(fact_156_eoutM__eout, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression]: (((((eoutM @ P) @ M) @ E) => ((eout @ P) @ E))))).
% 0.32/1.60  thf(fact_157_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))))).
% 0.32/1.60  thf(fact_158_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))))).
% 0.32/1.60  thf(fact_159_eout__def, axiom, (eout = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((exprChannel @ Ch3) @ E2)))))))).
% 0.32/1.60  thf(fact_160_TBtheorem5b__notP2, axiom, (! [Q:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((eoutM @ Q) @ M) @ 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) @ M) @ E))))))))))).
% 0.32/1.60  thf(fact_161_TBtheore54b__P, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ P) @ M) @ 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) @ M)))))) => (((eoutM @ PQ) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_162_TBtheorem5b__PQ, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((eoutM @ P) @ M) @ E) | (((eoutM @ Q) @ M) @ 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) @ M) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((eoutM @ PQ) @ M) @ E)))))))).
% 0.32/1.60  thf(fact_163_TBtheorem5b__notP1, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eoutM @ P) @ M) @ E) => ((~ ((((eoutM @ Q) @ M) @ 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) @ M) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((eoutM @ PQ) @ M) @ E))))))))))).
% 0.32/1.60  thf(fact_164_correctCompositionOut__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X3:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((member @ secrecy_chanID) @ X3) @ (out @ PQ)) => ((((member @ secrecy_chanID) @ X3) @ (out @ P)) | (((member @ secrecy_chanID) @ X3) @ (out @ Q))))))))).
% 0.32/1.60  thf(fact_165_outStream__def, axiom, (outStream = (^ [X2:secrecy_specID]: (((^ [Y:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y = Z))) @ (out @ X2)))))).
% 0.32/1.60  thf(fact_166_TBtheorem5b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M:(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) => ((M = (((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) @ M) @ E))))))))))))).
% 0.32/1.60  thf(fact_167_insert__subsetI, axiom, (! [A:$tType,X3:A,A3:(set @ A),X5:(set @ A)]: (((((member @ A) @ X3) @ A3) => ((((ord_less_eq @ (set @ A)) @ X5) @ A3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ X5)) @ A3)))))).
% 0.32/1.60  thf(fact_168_UnCI, axiom, (! [A:$tType,C:A,B:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C) @ B))) => (((member @ A) @ C) @ A3)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_169_Un__iff, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)) = ((((member @ A) @ C) @ A3) | (((member @ A) @ C) @ B)))))).
% 0.32/1.60  thf(fact_170_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B = (bot_bot @ (set @ A)))))))).
% 0.32/1.60  thf(fact_171_Un__insert__left, axiom, (! [A:$tType,A2:A,B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ B)) @ C4) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 0.32/1.60  thf(fact_172_Un__insert__right, axiom, (! [A:$tType,A3:(set @ A),A2:A,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B)) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_173_Un__subset__iff, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A3) @ C4) & (((ord_less_eq @ (set @ A)) @ B) @ C4)))))).
% 0.32/1.60  thf(fact_174_Un__empty__left, axiom, (! [A:$tType,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B) = B)))).
% 0.32/1.60  thf(fact_175_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 0.32/1.60  thf(fact_176_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B7:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B7) = B7))))))).
% 0.32/1.60  thf(fact_177_subset__UnE, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => (~ ((! [A7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ A3) => (! [B8:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B8) @ B) => (C4 != (((sup_sup @ (set @ A)) @ A7) @ B8)))))))))))))).
% 0.32/1.60  thf(fact_178_Un__absorb2, axiom, (! [A:$tType,B:(set @ A),A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B) @ A3) => ((((sup_sup @ (set @ A)) @ A3) @ B) = A3))))).
% 0.32/1.60  thf(fact_179_Un__absorb1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((sup_sup @ (set @ A)) @ A3) @ B) = B))))).
% 0.32/1.60  thf(fact_180_Un__upper2, axiom, (! [A:$tType,B:(set @ A),A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 0.32/1.60  thf(fact_181_Un__upper1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 0.32/1.60  thf(fact_182_Un__least, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4)))))).
% 0.32/1.60  thf(fact_183_Un__mono, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),B:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 0.32/1.60  thf(fact_184_ineM__Un1, axiom, (! [P:secrecy_specID,A3:(set @ secrecy_chanID),E:secrecy_Expression,B:(set @ secrecy_chanID)]: (((((ineM @ P) @ A3) @ E) => (((ineM @ P) @ (((sup_sup @ (set @ secrecy_chanID)) @ A3) @ B)) @ E))))).
% 0.32/1.60  thf(fact_185_UnE, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => ((~ ((((member @ A) @ C) @ A3))) => (((member @ A) @ C) @ B)))))).
% 0.32/1.60  thf(fact_186_UnI1, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_187_UnI2, axiom, (! [A:$tType,C:A,B:(set @ A),A3:(set @ A)]: (((((member @ A) @ C) @ B) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_188_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A3) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B) & (P @ X2))))))))).
% 0.32/1.60  thf(fact_189_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A3) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B) => (P @ X2))))))))).
% 0.32/1.60  thf(fact_190_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 0.32/1.60  thf(fact_191_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 0.32/1.60  thf(fact_192_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B7:(set @ A)]: ((((sup_sup @ (set @ A)) @ B7) @ A4))))))).
% 0.32/1.60  thf(fact_193_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B)) = (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 0.32/1.60  thf(fact_194_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)) = (((sup_sup @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A3) @ C4)))))).
% 0.32/1.60  thf(fact_195_singleton__Un__iff, axiom, (! [A:$tType,X3:A,A3:(set @ A),B:(set @ A)]: ((((((insert @ A) @ X3) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A3) @ B)) = (((A3 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 0.32/1.60  thf(fact_196_Un__singleton__iff, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),X3:A]: ((((((sup_sup @ (set @ A)) @ A3) @ B) = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = (((A3 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 0.32/1.60  thf(fact_197_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 0.32/1.60  thf(fact_198_subset__emptyI, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A3))))) => (((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))))))).
% 0.32/1.60  thf(fact_199_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 0.32/1.60  thf(fact_200_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A2) @ B2)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 0.32/1.60  thf(fact_201_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 0.32/1.60  thf(fact_202_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X3) @ Y3)) @ Z2) = ((((ord_less_eq @ A) @ X3) @ Z2) & (((ord_less_eq @ A) @ Y3) @ Z2))))))))).
% 0.32/1.60  thf(fact_203_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,C:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C)) @ A2) = ((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ C) @ A2))))))))).
% 0.32/1.60  thf(fact_204_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X3) = X3))))))).
% 0.32/1.60  thf(fact_205_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ (bot_bot @ A)) = X3))))))).
% 0.32/1.60  thf(fact_206_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X3) @ Y3)) = ((X3 = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 0.32/1.60  thf(fact_207_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y3:A]: ((((((sup_sup @ A) @ X3) @ Y3) = (bot_bot @ A)) = ((X3 = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 0.32/1.60  thf(fact_208_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((((sup_sup @ A) @ A2) @ B2) = (bot_bot @ A)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 0.32/1.60  thf(fact_209_inf__sup__ord_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [Y3:A,X3:A]: ((((ord_less_eq @ A) @ Y3) @ (((sup_sup @ A) @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_210_inf__sup__ord_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_211_le__supE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A,X3:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X3) => (~ (((((ord_less_eq @ A) @ A2) @ X3) => (~ ((((ord_less_eq @ A) @ B2) @ X3))))))))))))).
% 0.32/1.60  thf(fact_212_le__supI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,X3:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ X3) => ((((ord_less_eq @ A) @ B2) @ X3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X3))))))))).
% 0.32/1.60  thf(fact_213_sup__ge1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y3:A]: ((((ord_less_eq @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_214_sup__ge2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X3:A]: ((((ord_less_eq @ A) @ Y3) @ (((sup_sup @ A) @ X3) @ Y3)))))))).
% 0.32/1.60  thf(fact_215_le__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X3) @ A2) => (((ord_less_eq @ A) @ X3) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_216_le__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ X3) @ B2) => (((ord_less_eq @ A) @ X3) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_217_sup_Omono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C:A,A2:A,D:A,B2:A]: (((((ord_less_eq @ A) @ C) @ A2) => ((((ord_less_eq @ A) @ D) @ B2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C) @ D)) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 0.32/1.60  thf(fact_218_sup__mono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,C:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ (((sup_sup @ A) @ C) @ D)))))))))).
% 0.32/1.60  thf(fact_219_sup__least, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X3:A,Z2:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ Z2) @ X3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y3) @ Z2)) @ X3))))))))).
% 0.32/1.60  thf(fact_220_le__iff__sup, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [X2:A,Y4:A]: (((((sup_sup @ A) @ X2) @ Y4) = Y4)))))))).
% 0.32/1.60  thf(fact_221_sup_OorderE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_222_sup_OorderI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 0.32/1.60  thf(fact_223_sup__unique, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [F:(A > (A > A)),X3:A,Y3:A]: (((! [X4:A,Y2:A]: ((((ord_less_eq @ A) @ X4) @ ((F @ X4) @ Y2)))) => ((! [X4:A,Y2:A]: ((((ord_less_eq @ A) @ Y2) @ ((F @ X4) @ Y2)))) => ((! [X4:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ Y2) @ X4) => ((((ord_less_eq @ A) @ Z3) @ X4) => (((ord_less_eq @ A) @ ((F @ Y2) @ Z3)) @ X4))))) => ((((sup_sup @ A) @ X3) @ Y3) = ((F @ X3) @ Y3))))))))))).
% 0.32/1.60  thf(fact_224_sup_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((sup_sup @ A) @ A2) @ B2) = A2)))))))).
% 0.32/1.60  thf(fact_225_sup_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((sup_sup @ A) @ A2) @ B2) = B2)))))))).
% 0.32/1.60  thf(fact_226_sup__absorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((sup_sup @ A) @ X3) @ Y3) = X3)))))))).
% 0.32/1.60  thf(fact_227_sup__absorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((sup_sup @ A) @ X3) @ Y3) = Y3)))))))).
% 0.32/1.60  thf(fact_228_sup_OboundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,C:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C)) @ A2) => (~ (((((ord_less_eq @ A) @ B2) @ A2) => (~ ((((ord_less_eq @ A) @ C) @ A2))))))))))))).
% 0.32/1.60  thf(fact_229_sup_OboundedI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C)) @ A2))))))))).
% 0.32/1.60  thf(fact_230_sup_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: ((A5 = (((sup_sup @ A) @ A5) @ B5))))))))).
% 0.32/1.60  thf(fact_231_sup_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.32/1.60  thf(fact_232_sup_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: ((((ord_less_eq @ A) @ B2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.32/1.60  thf(fact_233_sup_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B5:A,A5:A]: (((((sup_sup @ A) @ A5) @ B5) = A5)))))))).
% 0.32/1.60  thf(fact_234_sup_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [A5:A,B5:A]: (((((sup_sup @ A) @ A5) @ B5) = B5)))))))).
% 0.32/1.60  thf(fact_235_sup_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C) @ A2) => (((ord_less_eq @ A) @ C) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_236_sup_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.32/1.60  thf(fact_237_correctInOutLoc__def, axiom, (correctInOutLoc = (^ [X2:secrecy_specID]: ((((((inf_inf @ (set @ secrecy_chanID)) @ (ins @ X2)) @ (out @ X2)) = (bot_bot @ (set @ secrecy_chanID))) & (((((inf_inf @ (set @ secrecy_chanID)) @ (ins @ X2)) @ (loc @ X2)) = (bot_bot @ (set @ secrecy_chanID))) & ((((inf_inf @ (set @ secrecy_chanID)) @ (loc @ X2)) @ (out @ X2)) = (bot_bot @ (set @ secrecy_chanID))))))))).
% 0.32/1.60  thf(fact_238_subset__Compl__singleton, axiom, (! [A:$tType,A3:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ ((uminus_uminus @ (set @ A)) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))) = (~ ((((member @ A) @ B2) @ A3))))))).
% 0.32/1.60  thf(fact_239_IntI, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ A3) => ((((member @ A) @ C) @ B) => (((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B))))))).
% 0.32/1.60  thf(fact_240_Int__iff, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B)) = ((((member @ A) @ C) @ A3) & (((member @ A) @ C) @ B)))))).
% 0.32/1.60  thf(fact_241_ComplI, axiom, (! [A:$tType,C:A,A3:(set @ A)]: (((~ ((((member @ A) @ C) @ A3))) => (((member @ A) @ C) @ ((uminus_uminus @ (set @ A)) @ A3)))))).
% 0.32/1.60  thf(fact_242_Compl__iff, axiom, (! [A:$tType,C:A,A3:(set @ A)]: (((((member @ A) @ C) @ ((uminus_uminus @ (set @ A)) @ A3)) = (~ ((((member @ A) @ C) @ A3))))))).
% 0.32/1.60  thf(fact_243_Compl__eq__Compl__iff, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A3) = ((uminus_uminus @ (set @ A)) @ B)) = (A3 = B))))).
% 0.32/1.60  thf(fact_244_compl__le__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X3)) @ ((uminus_uminus @ A) @ Y3)) = (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 0.32/1.60  thf(fact_245_le__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ (((inf_inf @ A) @ Y3) @ Z2)) = ((((ord_less_eq @ A) @ X3) @ Y3) & (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 0.32/1.60  thf(fact_246_inf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.60  thf(fact_247_inf__bot__left, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X3:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X3) = (bot_bot @ A)))))))).
% 0.32/1.60  thf(fact_248_inf__bot__right, axiom, (! [A:$tType]: (((bounded_lattice_bot @ A) => (! [X3:A]: (((((inf_inf @ A) @ X3) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 0.32/1.60  thf(fact_249_Int__insert__left__if0, axiom, (! [A:$tType,A2:A,C4:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ A2) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B)) @ C4) = (((inf_inf @ (set @ A)) @ B) @ C4)))))).
% 0.32/1.60  thf(fact_250_Int__insert__left__if1, axiom, (! [A:$tType,A2:A,C4:(set @ A),B:(set @ A)]: (((((member @ A) @ A2) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B)) @ C4) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ B) @ C4))))))).
% 0.32/1.60  thf(fact_251_insert__inter__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A),B:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A3)) @ (((insert @ A) @ A2) @ B)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_252_Int__insert__right__if0, axiom, (! [A:$tType,A2:A,A3:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((((inf_inf @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B)) = (((inf_inf @ (set @ A)) @ A3) @ B)))))).
% 0.32/1.60  thf(fact_253_Int__insert__right__if1, axiom, (! [A:$tType,A2:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((inf_inf @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A3) @ B))))))).
% 0.32/1.60  thf(fact_254_Int__subset__iff, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A3) @ B)) = ((((ord_less_eq @ (set @ A)) @ C4) @ A3) & (((ord_less_eq @ (set @ A)) @ C4) @ B)))))).
% 0.32/1.60  thf(fact_255_Int__Un__eq_I4_J, axiom, (! [A:$tType,T2:(set @ A),S:(set @ A)]: (((((sup_sup @ (set @ A)) @ T2) @ (((inf_inf @ (set @ A)) @ S) @ T2)) = T2)))).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice_bot @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_sup @ A9) => (semilattice_sup @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_inf @ A9) => (semilattice_inf @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A8:$tType,A9:$tType]: (((boolean_algebra @ A9) => (boolean_algebra @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A8:$tType,A9:$tType]: (((order_bot @ A9) => (order_bot @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: (((lattice @ A9) => (lattice @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 0.32/1.60  thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3, axiom, (semilattice_sup @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4, axiom, (semilattice_inf @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Oorder__bot_5, axiom, (order_bot @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Opreorder_6, axiom, (preorder @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Lattices_Olattice_7, axiom, (lattice @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Oorder_8, axiom, (order @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Oord_9, axiom, (ord @ nat)).
% 0.32/1.60  thf(tcon_Nat_Onat___Orderings_Obot_10, axiom, (bot @ nat)).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_11, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_12, axiom, (! [A8:$tType]: ((bounded_lattice_bot @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Osemilattice__sup_13, axiom, (! [A8:$tType]: ((semilattice_sup @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Osemilattice__inf_14, axiom, (! [A8:$tType]: ((semilattice_inf @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Oboolean__algebra_15, axiom, (! [A8:$tType]: ((boolean_algebra @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Orderings_Oorder__bot_16, axiom, (! [A8:$tType]: ((order_bot @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Orderings_Opreorder_17, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Lattices_Olattice_18, axiom, (! [A8:$tType]: ((lattice @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Orderings_Oorder_19, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Orderings_Oord_20, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.32/1.60  thf(tcon_Set_Oset___Orderings_Obot_21, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_22, axiom, (bounde1808546759up_bot @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_23, axiom, (bounded_lattice_bot @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_24, axiom, (semilattice_sup @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_25, axiom, (semilattice_inf @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_26, axiom, (boolean_algebra @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Oorder__bot_27, axiom, (order_bot @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Opreorder_28, axiom, (preorder @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Olinorder_29, axiom, (linorder @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Lattices_Olattice_30, axiom, (lattice @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Oorder_31, axiom, (order @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Oord_32, axiom, (ord @ $o)).
% 0.32/1.60  thf(tcon_HOL_Obool___Orderings_Obot_33, axiom, (bot @ $o)).
% 0.32/1.60  thf(conj_0, conjecture, (((member @ secrecy_chanID) @ ch) @ (loc @ pq))).
% 0.32/1.60  % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2DTF7835.p
% 0.32/1.60  ------------------------
% 0.32/1.64  ---- Cleaned THF ---
% 0.32/1.64  thf(ty_t_Secrecy__types_OExpression,type,
% 0.32/1.64      secrecy_Expression: $tType ).
% 0.32/1.64  
% 0.32/1.64  thf(ty_t_Secrecy__types_OspecID,type,
% 0.32/1.64      secrecy_specID: $tType ).
% 0.32/1.64  
% 0.32/1.64  thf(ty_t_Secrecy__types_OchanID,type,
% 0.32/1.64      secrecy_chanID: $tType ).
% 0.32/1.64  
% 0.32/1.64  thf(ty_t_Set_Oset,type,
% 0.32/1.64      set: $tType > $tType ).
% 0.32/1.64  
% 0.32/1.64  thf(ty_t_Nat_Onat,type,
% 0.32/1.64      nat: $tType ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.32/1.64      bounded_lattice: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_HOL_Otype,type,
% 0.32/1.64      type: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Obot,type,
% 0.32/1.64      bot: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Oord,type,
% 0.32/1.64      ord: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Oorder,type,
% 0.32/1.64      order: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Olattice,type,
% 0.32/1.64      lattice: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Olinorder,type,
% 0.32/1.64      linorder: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Opreorder,type,
% 0.32/1.64      preorder: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Orderings_Oorder__bot,type,
% 0.32/1.64      order_bot: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.32/1.64      boolean_algebra: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.32/1.64      semilattice_inf: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.32/1.64      semilattice_sup: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.32/1.64      bounded_lattice_bot: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.32/1.64      bounde1808546759up_bot: 
% 0.32/1.64        !>[A: $tType] : $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.32/1.64      uminus_uminus: 
% 0.32/1.64        !>[A: $tType] : ( A > A ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.32/1.64      inf_inf: 
% 0.32/1.64        !>[A: $tType] : ( A > A > A ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.32/1.64      sup_sup: 
% 0.32/1.64        !>[A: $tType] : ( A > A > A ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.32/1.64      bot_bot: 
% 0.32/1.64        !>[A: $tType] : A ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.32/1.64      ord_less_eq: 
% 0.32/1.64        !>[A: $tType] : ( A > A > $o ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oeout,type,
% 0.32/1.64      eout: secrecy_specID > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_OeoutM,type,
% 0.32/1.64      eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_OexprChannel,type,
% 0.32/1.64      exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oine,type,
% 0.32/1.64      ine: secrecy_specID > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_OineM,type,
% 0.32/1.64      ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.32/1.64      ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.32/1.64      ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.32/1.64      out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.32/1.64      out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_OCollect,type,
% 0.32/1.64      collect: 
% 0.32/1.64        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_Oinsert,type,
% 0.32/1.64      insert: 
% 0.32/1.64        !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_Ois__empty,type,
% 0.32/1.64      is_empty: 
% 0.32/1.64        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_Ois__singleton,type,
% 0.32/1.64      is_singleton: 
% 0.32/1.64        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_Opairwise,type,
% 0.32/1.64      pairwise: 
% 0.32/1.64        !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_Set_Othe__elem,type,
% 0.32/1.64      the_elem: 
% 0.32/1.64        !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.32/1.64      correctCompositionIn: secrecy_specID > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.32/1.64      correc965049635ionLoc: secrecy_specID > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.32/1.64      correc990227761ionOut: secrecy_specID > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OcorrectInOutLoc,type,
% 0.32/1.64      correctInOutLoc: secrecy_specID > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OinStream,type,
% 0.32/1.64      inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_Oins,type,
% 0.32/1.64      ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_Oloc,type,
% 0.32/1.64      loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OlocStream,type,
% 0.32/1.64      locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_Oout,type,
% 0.32/1.64      out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_OoutStream,type,
% 0.32/1.64      outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_inout_Osubcomponents,type,
% 0.32/1.64      subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_c_member,type,
% 0.32/1.64      member: 
% 0.32/1.64        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_v_P,type,
% 0.32/1.64      p: secrecy_specID ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_v_PQ,type,
% 0.32/1.64      pq: secrecy_specID ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_v_Q,type,
% 0.32/1.64      q: secrecy_specID ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_v_ch,type,
% 0.32/1.64      ch: secrecy_chanID ).
% 0.32/1.64  
% 0.32/1.64  thf(sy_v_m,type,
% 0.32/1.64      m: secrecy_Expression ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_0_assms_I2_J,axiom,
% 0.32/1.64      correctCompositionIn @ pq ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_1_assms_I4_J,axiom,
% 0.32/1.64      exprChannel @ ch @ m ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_2_assms_I3_J,axiom,
% 0.32/1.64      member @ secrecy_chanID @ ch @ ( ins @ p ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_3_assms_I5_J,axiom,
% 0.32/1.64      ! [X: secrecy_chanID] :
% 0.32/1.64        ( ( member @ secrecy_chanID @ X @ ( ins @ pq ) )
% 0.32/1.64       => ~ ( exprChannel @ X @ m ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_4_assms_I1_J,axiom,
% 0.32/1.64      ( ( subcomponents @ pq )
% 0.32/1.64      = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_5_locStream__def,axiom,
% 0.32/1.64      ( locStream
% 0.32/1.64      = ( ^ [X2: secrecy_specID] :
% 0.32/1.64            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.32/1.64            @ ( loc @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_6_correctCompositionIn__L1,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correctCompositionIn @ PQ )
% 0.32/1.64         => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.32/1.64           => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.32/1.64             => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_7_correctCompositionIn__L2,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correctCompositionIn @ PQ )
% 0.32/1.64         => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.32/1.64           => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.32/1.64              | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_8_correctCompositionIn__prop1,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correctCompositionIn @ PQ )
% 0.32/1.64         => ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 0.32/1.64           => ( ( member @ secrecy_chanID @ X3 @ ( ins @ P ) )
% 0.32/1.64              | ( member @ secrecy_chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_9_singletonI,axiom,
% 0.32/1.64      ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_10_TBtheorem4b__P,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( ineM @ P @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.32/1.64                  & ( member @ secrecy_chanID @ Ch2 @ M ) )
% 0.32/1.64             => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_11_TBtheorem4b__PQ,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( ineM @ P @ M @ E )
% 0.32/1.64          | ( ineM @ Q @ M @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.32/1.64                    | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.32/1.64                  & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_12_TBlemma3b,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.32/1.64        ( ~ ( ineM @ P @ M @ E )
% 0.32/1.64       => ( ~ ( ineM @ Q @ M @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correctCompositionIn @ PQ )
% 0.32/1.64             => ( ( member @ secrecy_chanID @ Ch @ M )
% 0.32/1.64               => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.32/1.64                 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_13_inStream__def,axiom,
% 0.32/1.64      ( inStream
% 0.32/1.64      = ( ^ [X2: secrecy_specID] :
% 0.32/1.64            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.32/1.64            @ ( ins @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_14_insertCI,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.32/1.64        ( ( ~ ( member @ A @ A2 @ B )
% 0.32/1.64         => ( A2 = B2 ) )
% 0.32/1.64       => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_15_insert__iff,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.32/1.64        = ( ( A2 = B2 )
% 0.32/1.64          | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_16_insert__absorb2,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A] :
% 0.32/1.64        ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A3 ) )
% 0.32/1.64        = ( insert @ A @ X3 @ A3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_17_empty__iff,axiom,
% 0.32/1.64      ! [A: $tType,C: A] :
% 0.32/1.64        ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_18_all__not__in__conv,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( ! [X2: A] :
% 0.32/1.64              ~ ( member @ A @ X2 @ A3 ) )
% 0.32/1.64        = ( A3
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_19_Collect__empty__eq,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o] :
% 0.32/1.64        ( ( ( collect @ A @ P )
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64        = ( ! [X2: A] :
% 0.32/1.64              ~ ( P @ X2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_20_empty__Collect__eq,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o] :
% 0.32/1.64        ( ( ( bot_bot @ ( set @ A ) )
% 0.32/1.64          = ( collect @ A @ P ) )
% 0.32/1.64        = ( ! [X2: A] :
% 0.32/1.64              ~ ( P @ X2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_21_ineM__def,axiom,
% 0.32/1.64      ( ineM
% 0.32/1.64      = ( ^ [SP: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64          ? [Ch3: secrecy_chanID] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.32/1.64            & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_22_ineM__L1,axiom,
% 0.32/1.64      ! [Ch: secrecy_chanID,M: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.32/1.64        ( ( member @ secrecy_chanID @ Ch @ M )
% 0.32/1.64       => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.32/1.64         => ( ( exprChannel @ Ch @ E )
% 0.32/1.64           => ( ineM @ P @ M @ E ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_23_ex__in__conv,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.32/1.64        = ( A3
% 0.32/1.64         != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_24_equals0I,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ! [Y2: A] :
% 0.32/1.64            ~ ( member @ A @ Y2 @ A3 )
% 0.32/1.64       => ( A3
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_25_equals0D,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,A2: A] :
% 0.32/1.64        ( ( A3
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64       => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_26_emptyE,axiom,
% 0.32/1.64      ! [A: $tType,A2: A] :
% 0.32/1.64        ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_27_mk__disjoint__insert,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ A3 )
% 0.32/1.64       => ? [B3: set @ A] :
% 0.32/1.64            ( ( A3
% 0.32/1.64              = ( insert @ A @ A2 @ B3 ) )
% 0.32/1.64            & ~ ( member @ A @ A2 @ B3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_28_insert__commute,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,Y3: A,A3: set @ A] :
% 0.32/1.64        ( ( insert @ A @ X3 @ ( insert @ A @ Y3 @ A3 ) )
% 0.32/1.64        = ( insert @ A @ Y3 @ ( insert @ A @ X3 @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_29_insert__eq__iff,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A,B2: A,B: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ A2 @ A3 )
% 0.32/1.64       => ( ~ ( member @ A @ B2 @ B )
% 0.32/1.64         => ( ( ( insert @ A @ A2 @ A3 )
% 0.32/1.64              = ( insert @ A @ B2 @ B ) )
% 0.32/1.64            = ( ( ( A2 = B2 )
% 0.32/1.64               => ( A3 = B ) )
% 0.32/1.64              & ( ( A2 != B2 )
% 0.32/1.64               => ? [C2: set @ A] :
% 0.32/1.64                    ( ( A3
% 0.32/1.64                      = ( insert @ A @ B2 @ C2 ) )
% 0.32/1.64                    & ~ ( member @ A @ B2 @ C2 )
% 0.32/1.64                    & ( B
% 0.32/1.64                      = ( insert @ A @ A2 @ C2 ) )
% 0.32/1.64                    & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_30_insert__absorb,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ A3 )
% 0.32/1.64       => ( ( insert @ A @ A2 @ A3 )
% 0.32/1.64          = A3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_31_insert__ident,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ X3 @ A3 )
% 0.32/1.64       => ( ~ ( member @ A @ X3 @ B )
% 0.32/1.64         => ( ( ( insert @ A @ X3 @ A3 )
% 0.32/1.64              = ( insert @ A @ X3 @ B ) )
% 0.32/1.64            = ( A3 = B ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_32_Set_Oset__insert,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ X3 @ A3 )
% 0.32/1.64       => ~ ! [B3: set @ A] :
% 0.32/1.64              ( ( A3
% 0.32/1.64                = ( insert @ A @ X3 @ B3 ) )
% 0.32/1.64             => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_33_insertI2,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.32/1.64        ( ( member @ A @ A2 @ B )
% 0.32/1.64       => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_34_insertI1,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_35_insertE,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.32/1.64       => ( ( A2 != B2 )
% 0.32/1.64         => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_36_TBtheorem3b,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ~ ( ineM @ P @ M @ E )
% 0.32/1.64       => ( ~ ( ineM @ Q @ M @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correctCompositionIn @ PQ )
% 0.32/1.64             => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_37_TBtheorem1b,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( ineM @ PQ @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ( ineM @ P @ M @ E )
% 0.32/1.64              | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_38_singleton__inject,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B2: A] :
% 0.32/1.64        ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64       => ( A2 = B2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_39_insert__not__empty,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A] :
% 0.32/1.64        ( ( insert @ A @ A2 @ A3 )
% 0.32/1.64       != ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_40_doubleton__eq__iff,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B2: A,C: A,D: A] :
% 0.32/1.64        ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64          = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/1.64        = ( ( ( A2 = C )
% 0.32/1.64            & ( B2 = D ) )
% 0.32/1.64          | ( ( A2 = D )
% 0.32/1.64            & ( B2 = C ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_41_singleton__iff,axiom,
% 0.32/1.64      ! [A: $tType,B2: A,A2: A] :
% 0.32/1.64        ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64        = ( B2 = A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_42_singletonD,axiom,
% 0.32/1.64      ! [A: $tType,B2: A,A2: A] :
% 0.32/1.64        ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64       => ( B2 = A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_43_TBtheorem4b__notP1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ineM @ P @ M @ E )
% 0.32/1.64       => ( ~ ( ineM @ Q @ M @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correctCompositionIn @ PQ )
% 0.32/1.64             => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                    ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_44_TBtheorem4b__notPQ,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correctCompositionIn @ PQ )
% 0.32/1.64         => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.32/1.64           => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/1.64                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64                 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_45_mem__Collect__eq,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,P: A > $o] :
% 0.32/1.64        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/1.64        = ( P @ A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_46_Collect__mem__eq,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( collect @ A
% 0.32/1.64          @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.32/1.64        = A3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_47_Collect__cong,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/1.64        ( ! [X4: A] :
% 0.32/1.64            ( ( P @ X4 )
% 0.32/1.64            = ( Q @ X4 ) )
% 0.32/1.64       => ( ( collect @ A @ P )
% 0.32/1.64          = ( collect @ A @ Q ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_48_ext,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 0.32/1.64        ( ! [X4: A] :
% 0.32/1.64            ( ( F @ X4 )
% 0.32/1.64            = ( G @ X4 ) )
% 0.32/1.64       => ( F = G ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_49_TBtheorem4b__notP2,axiom,
% 0.32/1.64      ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( ineM @ Q @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_50_the__elem__eq,axiom,
% 0.32/1.64      ! [A: $tType,X3: A] :
% 0.32/1.64        ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64        = X3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_51_bot__apply,axiom,
% 0.32/1.64      ! [C3: $tType,D2: $tType] :
% 0.32/1.64        ( ( bot @ C3 )
% 0.32/1.64       => ( ( bot_bot @ ( D2 > C3 ) )
% 0.32/1.64          = ( ^ [X2: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_52_TBtheorem4a__PQ,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( ine @ P @ E )
% 0.32/1.64          | ( ine @ Q @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.32/1.64                    | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_53_TBtheorem4a__P,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( ine @ P @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_54_is__singletonI,axiom,
% 0.32/1.64      ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_55_TBtheorem4a__empty,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( ine @ P @ E )
% 0.32/1.64          | ( ine @ Q @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ( ( loc @ PQ )
% 0.32/1.64                = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64             => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_56_ine__exprChannelSingle__def,axiom,
% 0.32/1.64      ( ine_ex1303305700Single
% 0.32/1.64      = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 )
% 0.32/1.64            & ! [X2: secrecy_chanID,T: nat] :
% 0.32/1.64                ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.32/1.64                  & ( X2 != Ch3 ) )
% 0.32/1.64               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_57_ine__empty__exprChannelSet,axiom,
% 0.32/1.64      ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64       => ( ( ChSet
% 0.32/1.64            = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64         => ~ ( ine @ P @ E ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_58_ine__exprChannelSet__Single,axiom,
% 0.32/1.64      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.32/1.64       => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_59_ine__exprChannelSingle__Set,axiom,
% 0.32/1.64      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.32/1.64       => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_60_ine__nonempty__exprChannelSet,axiom,
% 0.32/1.64      ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64       => ( ( ChSet
% 0.32/1.64           != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64         => ( ine @ P @ E ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_61_bot__set__def,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bot_bot @ ( set @ A ) )
% 0.32/1.64        = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_62_not__ine__ineM,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( ine @ P @ E )
% 0.32/1.64       => ~ ( ineM @ P @ M @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_63_ineM__ine,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( ineM @ P @ M @ E )
% 0.32/1.64       => ( ine @ P @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_64_is__singleton__the__elem,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( is_singleton @ A )
% 0.32/1.64        = ( ^ [A4: set @ A] :
% 0.32/1.64              ( A4
% 0.32/1.64              = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_65_ine__def,axiom,
% 0.32/1.64      ( ine
% 0.32/1.64      = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.32/1.64          ? [Ch3: secrecy_chanID] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_66_ine__ins__neg1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M3: secrecy_Expression,X3: secrecy_chanID] :
% 0.32/1.64        ( ~ ( ine @ P @ M3 )
% 0.32/1.64       => ( ( exprChannel @ X3 @ M3 )
% 0.32/1.64         => ~ ( member @ secrecy_chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_67_is__singletonI_H,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( A3
% 0.32/1.64         != ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64       => ( ! [X4: A,Y2: A] :
% 0.32/1.64              ( ( member @ A @ X4 @ A3 )
% 0.32/1.64             => ( ( member @ A @ Y2 @ A3 )
% 0.32/1.64               => ( X4 = Y2 ) ) )
% 0.32/1.64         => ( is_singleton @ A @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_68_bot__fun__def,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType] :
% 0.32/1.64        ( ( bot @ B4 )
% 0.32/1.64       => ( ( bot_bot @ ( A > B4 ) )
% 0.32/1.64          = ( ^ [X2: A] : ( bot_bot @ B4 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_69_TBtheorem4a__notP2,axiom,
% 0.32/1.64      ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( ine @ Q @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_70_TBtheorem4a__notPQ,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correctCompositionIn @ PQ )
% 0.32/1.64         => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.32/1.64           => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/1.64                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64                 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_71_TBtheorem4a__notP1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ine @ P @ E )
% 0.32/1.64       => ( ~ ( ine @ Q @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correctCompositionIn @ PQ )
% 0.32/1.64             => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                    ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_72_ine__exprChannelSet__def,axiom,
% 0.32/1.64      ( ine_exprChannelSet
% 0.32/1.64      = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64            ( ! [X2: secrecy_chanID] :
% 0.32/1.64                ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/1.64               => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.32/1.64                  & ( exprChannel @ X2 @ E2 ) ) )
% 0.32/1.64            & ! [X2: secrecy_chanID] :
% 0.32/1.64                ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/1.64                  & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 0.32/1.64               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_73_is__singletonE,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( is_singleton @ A @ A3 )
% 0.32/1.64       => ~ ! [X4: A] :
% 0.32/1.64              ( A3
% 0.32/1.64             != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_74_is__singleton__def,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( is_singleton @ A )
% 0.32/1.64        = ( ^ [A4: set @ A] :
% 0.32/1.64            ? [X2: A] :
% 0.32/1.64              ( A4
% 0.32/1.64              = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_75_TBtheorem1a,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( ine @ PQ @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correctCompositionIn @ PQ )
% 0.32/1.64           => ( ( ine @ P @ E )
% 0.32/1.64              | ( ine @ Q @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_76_TBtheorem3a,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ~ ( ine @ P @ E )
% 0.32/1.64       => ( ~ ( ine @ Q @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correctCompositionIn @ PQ )
% 0.32/1.64             => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_77_subcomponents__loc,axiom,
% 0.32/1.64      ! [X3: secrecy_specID] :
% 0.32/1.64        ( ( correc965049635ionLoc @ X3 )
% 0.32/1.64       => ( ( ( subcomponents @ X3 )
% 0.32/1.64            = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.32/1.64         => ( ( loc @ X3 )
% 0.32/1.64            = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_78_Set_Ois__empty__def,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( is_empty @ A )
% 0.32/1.64        = ( ^ [A4: set @ A] :
% 0.32/1.64              ( A4
% 0.32/1.64              = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_79_TBtheorem5a__empty,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( eout @ P @ E )
% 0.32/1.64          | ( eout @ Q @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ( ( loc @ PQ )
% 0.32/1.64                = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_80_bot__empty__eq,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bot_bot @ ( A > $o ) )
% 0.32/1.64        = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_81_Collect__empty__eq__bot,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o] :
% 0.32/1.64        ( ( ( collect @ A @ P )
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64        = ( P
% 0.32/1.64          = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_82_pairwise__singleton,axiom,
% 0.32/1.64      ! [A: $tType,P: A > A > $o,A3: A] : ( pairwise @ A @ P @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_83_singleton__insert__inj__eq,axiom,
% 0.32/1.64      ! [A: $tType,B2: A,A2: A,A3: set @ A] :
% 0.32/1.64        ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          = ( insert @ A @ A2 @ A3 ) )
% 0.32/1.64        = ( ( A2 = B2 )
% 0.32/1.64          & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_84_order__refl,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( preorder @ A )
% 0.32/1.64       => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_85_subsetI,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ! [X4: A] :
% 0.32/1.64            ( ( member @ A @ X4 @ A3 )
% 0.32/1.64           => ( member @ A @ X4 @ B ) )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_86_subset__antisym,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/1.64         => ( A3 = B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_87_empty__subsetI,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_88_subset__empty,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64        = ( A3
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_89_insert__subset,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A3 ) @ B )
% 0.32/1.64        = ( ( member @ A @ X3 @ B )
% 0.32/1.64          & ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_90_singleton__insert__inj__eq_H,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A,B2: A] :
% 0.32/1.64        ( ( ( insert @ A @ A2 @ A3 )
% 0.32/1.64          = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64        = ( ( A2 = B2 )
% 0.32/1.64          & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_91_le__funD,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType] :
% 0.32/1.64        ( ( ord @ B4 )
% 0.32/1.64       => ! [F: A > B4,G: A > B4,X3: A] :
% 0.32/1.64            ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.32/1.64           => ( ord_less_eq @ B4 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_92_le__funE,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType] :
% 0.32/1.64        ( ( ord @ B4 )
% 0.32/1.64       => ! [F: A > B4,G: A > B4,X3: A] :
% 0.32/1.64            ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.32/1.64           => ( ord_less_eq @ B4 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_93_le__funI,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType] :
% 0.32/1.64        ( ( ord @ B4 )
% 0.32/1.64       => ! [F: A > B4,G: A > B4] :
% 0.32/1.64            ( ! [X4: A] : ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.32/1.64           => ( ord_less_eq @ ( A > B4 ) @ F @ G ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_94_le__fun__def,axiom,
% 0.32/1.64      ! [B4: $tType,A: $tType] :
% 0.32/1.64        ( ( ord @ B4 )
% 0.32/1.64       => ( ( ord_less_eq @ ( A > B4 ) )
% 0.32/1.64          = ( ^ [F2: A > B4,G2: A > B4] :
% 0.32/1.64              ! [X2: A] : ( ord_less_eq @ B4 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_95_order__subst1,axiom,
% 0.32/1.64      ! [A: $tType,B4: $tType] :
% 0.32/1.64        ( ( ( order @ B4 )
% 0.32/1.64          & ( order @ A ) )
% 0.32/1.64       => ! [A2: A,F: B4 > A,B2: B4,C: B4] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.32/1.64           => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.32/1.64             => ( ! [X4: B4,Y2: B4] :
% 0.32/1.64                    ( ( ord_less_eq @ B4 @ X4 @ Y2 )
% 0.32/1.64                   => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/1.64               => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_96_order__subst2,axiom,
% 0.32/1.64      ! [A: $tType,C3: $tType] :
% 0.32/1.64        ( ( ( order @ C3 )
% 0.32/1.64          & ( order @ A ) )
% 0.32/1.64       => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 0.32/1.64             => ( ! [X4: A,Y2: A] :
% 0.32/1.64                    ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.32/1.64                   => ( ord_less_eq @ C3 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/1.64               => ( ord_less_eq @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_97_ord__eq__le__subst,axiom,
% 0.32/1.64      ! [A: $tType,B4: $tType] :
% 0.32/1.64        ( ( ( ord @ B4 )
% 0.32/1.64          & ( ord @ A ) )
% 0.32/1.64       => ! [A2: A,F: B4 > A,B2: B4,C: B4] :
% 0.32/1.64            ( ( A2
% 0.32/1.64              = ( F @ B2 ) )
% 0.32/1.64           => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.32/1.64             => ( ! [X4: B4,Y2: B4] :
% 0.32/1.64                    ( ( ord_less_eq @ B4 @ X4 @ Y2 )
% 0.32/1.64                   => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/1.64               => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_98_ord__le__eq__subst,axiom,
% 0.32/1.64      ! [A: $tType,B4: $tType] :
% 0.32/1.64        ( ( ( ord @ B4 )
% 0.32/1.64          & ( ord @ A ) )
% 0.32/1.64       => ! [A2: A,B2: A,F: A > B4,C: B4] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( ( F @ B2 )
% 0.32/1.64                = C )
% 0.32/1.64             => ( ! [X4: A,Y2: A] :
% 0.32/1.64                    ( ( ord_less_eq @ A @ X4 @ Y2 )
% 0.32/1.64                   => ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.32/1.64               => ( ord_less_eq @ B4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_99_eq__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/1.64          = ( ^ [X2: A,Y4: A] :
% 0.32/1.64                ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.32/1.64                & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_100_antisym,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/1.64             => ( X3 = Y3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_101_linear,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( linorder @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64            | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_102_eq__refl,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( preorder @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( X3 = Y3 )
% 0.32/1.64           => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_103_le__cases,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( linorder @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64           => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_104_order_Otrans,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [A2: A,B2: A,C: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/1.64             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_105_le__cases3,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( linorder @ A )
% 0.32/1.64       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/1.64            ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64             => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.32/1.64           => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/1.64               => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.32/1.64             => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.32/1.64                 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.32/1.64               => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.32/1.64                   => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.32/1.64                 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.32/1.64                     => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.32/1.64                   => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.32/1.64                       => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_106_antisym__conv,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [Y3: A,X3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64              = ( X3 = Y3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_107_order__class_Oorder_Oeq__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/1.64          = ( ^ [A5: A,B5: A] :
% 0.32/1.64                ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.32/1.64                & ( ord_less_eq @ A @ B5 @ A5 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_108_ord__eq__le__trans,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ord @ A )
% 0.32/1.64       => ! [A2: A,B2: A,C: A] :
% 0.32/1.64            ( ( A2 = B2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/1.64             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_109_ord__le__eq__trans,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ord @ A )
% 0.32/1.64       => ! [A2: A,B2: A,C: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( B2 = C )
% 0.32/1.64             => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_110_order__class_Oorder_Oantisym,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [A2: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64             => ( A2 = B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_111_order__trans,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( preorder @ A )
% 0.32/1.64       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.32/1.64             => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_112_dual__order_Orefl,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_113_linorder__wlog,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( linorder @ A )
% 0.32/1.64       => ! [P: A > A > $o,A2: A,B2: A] :
% 0.32/1.64            ( ! [A6: A,B6: A] :
% 0.32/1.64                ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.32/1.64               => ( P @ A6 @ B6 ) )
% 0.32/1.64           => ( ! [A6: A,B6: A] :
% 0.32/1.64                  ( ( P @ B6 @ A6 )
% 0.32/1.64                 => ( P @ A6 @ B6 ) )
% 0.32/1.64             => ( P @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_114_dual__order_Otrans,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [B2: A,A2: A,C: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ C @ B2 )
% 0.32/1.64             => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_115_dual__order_Oeq__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ( ( ^ [Y: A,Z: A] : ( Y = Z ) )
% 0.32/1.64          = ( ^ [A5: A,B5: A] :
% 0.32/1.64                ( ( ord_less_eq @ A @ B5 @ A5 )
% 0.32/1.64                & ( ord_less_eq @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_116_dual__order_Oantisym,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order @ A )
% 0.32/1.64       => ! [B2: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64             => ( A2 = B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_117_in__mono,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,X3: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ( member @ A @ X3 @ A3 )
% 0.32/1.64         => ( member @ A @ X3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_118_subsetD,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,C: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ( member @ A @ C @ A3 )
% 0.32/1.64         => ( member @ A @ C @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_119_equalityE,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( A3 = B )
% 0.32/1.64       => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64           => ~ ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_120_pairwiseD,axiom,
% 0.32/1.64      ! [A: $tType,R: A > A > $o,S: set @ A,X3: A,Y3: A] :
% 0.32/1.64        ( ( pairwise @ A @ R @ S )
% 0.32/1.64       => ( ( member @ A @ X3 @ S )
% 0.32/1.64         => ( ( member @ A @ Y3 @ S )
% 0.32/1.64           => ( ( X3 != Y3 )
% 0.32/1.64             => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_121_pairwiseI,axiom,
% 0.32/1.64      ! [A: $tType,S: set @ A,R: A > A > $o] :
% 0.32/1.64        ( ! [X4: A,Y2: A] :
% 0.32/1.64            ( ( member @ A @ X4 @ S )
% 0.32/1.64           => ( ( member @ A @ Y2 @ S )
% 0.32/1.64             => ( ( X4 != Y2 )
% 0.32/1.64               => ( R @ X4 @ Y2 ) ) ) )
% 0.32/1.64       => ( pairwise @ A @ R @ S ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_122_subset__eq,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/1.64        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/1.64            ! [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ A4 )
% 0.32/1.64             => ( member @ A @ X2 @ B7 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_123_equalityD1,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( A3 = B )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_124_equalityD2,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( A3 = B )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_125_subset__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/1.64        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/1.64            ! [T: A] :
% 0.32/1.64              ( ( member @ A @ T @ A4 )
% 0.32/1.64             => ( member @ A @ T @ B7 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_126_subset__refl,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_127_Collect__mono,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/1.64        ( ! [X4: A] :
% 0.32/1.64            ( ( P @ X4 )
% 0.32/1.64           => ( Q @ X4 ) )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_128_pairwise__def,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( pairwise @ A )
% 0.32/1.64        = ( ^ [R2: A > A > $o,S2: set @ A] :
% 0.32/1.64            ! [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ S2 )
% 0.32/1.64             => ! [Y4: A] :
% 0.32/1.64                  ( ( member @ A @ Y4 @ S2 )
% 0.32/1.64                 => ( ( X2 != Y4 )
% 0.32/1.64                   => ( R2 @ X2 @ Y4 ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_129_subset__trans,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.32/1.64         => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_130_pairwise__mono,axiom,
% 0.32/1.64      ! [A: $tType,P: A > A > $o,A3: set @ A,Q: A > A > $o,B: set @ A] :
% 0.32/1.64        ( ( pairwise @ A @ P @ A3 )
% 0.32/1.64       => ( ! [X4: A,Y2: A] :
% 0.32/1.64              ( ( P @ X4 @ Y2 )
% 0.32/1.64             => ( Q @ X4 @ Y2 ) )
% 0.32/1.64         => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/1.64           => ( pairwise @ A @ Q @ B ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_131_set__eq__subset,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ^ [Y: set @ A,Z: set @ A] : ( Y = Z ) )
% 0.32/1.64        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/1.64              ( ( ord_less_eq @ ( set @ A ) @ A4 @ B7 )
% 0.32/1.64              & ( ord_less_eq @ ( set @ A ) @ B7 @ A4 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_132_pairwise__subset,axiom,
% 0.32/1.64      ! [A: $tType,P: A > A > $o,S: set @ A,T2: set @ A] :
% 0.32/1.64        ( ( pairwise @ A @ P @ S )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ T2 @ S )
% 0.32/1.64         => ( pairwise @ A @ P @ T2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_133_Collect__mono__iff,axiom,
% 0.32/1.64      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.32/1.64        = ( ! [X2: A] :
% 0.32/1.64              ( ( P @ X2 )
% 0.32/1.64             => ( Q @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_134_bot_Oextremum__uniqueI,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order_bot @ A )
% 0.32/1.64       => ! [A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/1.64           => ( A2
% 0.32/1.64              = ( bot_bot @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_135_bot_Oextremum__unique,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order_bot @ A )
% 0.32/1.64       => ! [A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/1.64            = ( A2
% 0.32/1.64              = ( bot_bot @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_136_bot_Oextremum,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( order_bot @ A )
% 0.32/1.64       => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_137_subset__insertI2,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,B2: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_138_subset__insertI,axiom,
% 0.32/1.64      ! [A: $tType,B: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A2 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_139_subset__insert,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ X3 @ A3 )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ B ) )
% 0.32/1.64          = ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_140_insert__mono,axiom,
% 0.32/1.64      ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_141_pairwise__empty,axiom,
% 0.32/1.64      ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_142_pairwise__insert,axiom,
% 0.32/1.64      ! [A: $tType,R3: A > A > $o,X3: A,S3: set @ A] :
% 0.32/1.64        ( ( pairwise @ A @ R3 @ ( insert @ A @ X3 @ S3 ) )
% 0.32/1.64        = ( ! [Y4: A] :
% 0.32/1.64              ( ( ( member @ A @ Y4 @ S3 )
% 0.32/1.64                & ( Y4 != X3 ) )
% 0.32/1.64             => ( ( R3 @ X3 @ Y4 )
% 0.32/1.64                & ( R3 @ Y4 @ X3 ) ) )
% 0.32/1.64          & ( pairwise @ A @ R3 @ S3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_143_subset__singleton__iff,axiom,
% 0.32/1.64      ! [A: $tType,X5: set @ A,A2: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ X5 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64        = ( ( X5
% 0.32/1.64            = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          | ( X5
% 0.32/1.64            = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_144_subset__singletonD,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,X3: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64       => ( ( A3
% 0.32/1.64            = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          | ( A3
% 0.32/1.64            = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_145_TBtheorem2a,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( eout @ PQ @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ( eout @ P @ E )
% 0.32/1.64              | ( eout @ Q @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_146_TBtheorem5a__notP1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( eout @ P @ E )
% 0.32/1.64       => ( ~ ( eout @ Q @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64             => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                    ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_147_TBtheorem5a__notPQ,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64         => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.32/1.64           => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                      ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/1.64                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64                 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_148_TBtheorem5a__notP2,axiom,
% 0.32/1.64      ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( eout @ Q @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_149_TBtheorem5a__PQ,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( eout @ P @ E )
% 0.32/1.64          | ( eout @ Q @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/1.64                    | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_150_TBtheorem45a__P,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( eout @ P @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_151_TBtheorem2b,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( eoutM @ PQ @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ( eoutM @ P @ M @ E )
% 0.32/1.64              | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_152_eoutM__def,axiom,
% 0.32/1.64      ( eoutM
% 0.32/1.64      = ( ^ [SP: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64          ? [Ch3: secrecy_chanID] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/1.64            & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_153_out__exprChannelSet__def,axiom,
% 0.32/1.64      ( out_exprChannelSet
% 0.32/1.64      = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64            ( ! [X2: secrecy_chanID] :
% 0.32/1.64                ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/1.64               => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.32/1.64                  & ( exprChannel @ X2 @ E2 ) ) )
% 0.32/1.64            & ! [X2: secrecy_chanID] :
% 0.32/1.64                ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.32/1.64                  & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 0.32/1.64               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_154_out__exprChannelSingle__def,axiom,
% 0.32/1.64      ( out_ex985543062Single
% 0.32/1.64      = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 )
% 0.32/1.64            & ! [X2: secrecy_chanID,T: nat] :
% 0.32/1.64                ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.32/1.64                  & ( X2 != Ch3 ) )
% 0.32/1.64               => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_155_not__eout__eoutM,axiom,
% 0.32/1.64      ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( eout @ P @ E )
% 0.32/1.64       => ~ ( eoutM @ P @ M @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_156_eoutM__eout,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( eoutM @ P @ M @ E )
% 0.32/1.64       => ( eout @ P @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_157_out__exprChannelSet__Single,axiom,
% 0.32/1.64      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.32/1.64       => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_158_out__exprChannelSingle__Set,axiom,
% 0.32/1.64      ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.32/1.64        ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.32/1.64       => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_159_eout__def,axiom,
% 0.32/1.64      ( eout
% 0.32/1.64      = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.32/1.64          ? [Ch3: secrecy_chanID] :
% 0.32/1.64            ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.32/1.64            & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_160_TBtheorem5b__notP2,axiom,
% 0.32/1.64      ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.32/1.64        ( ~ ( eoutM @ Q @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.32/1.64             => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                    ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.32/1.64                   => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_161_TBtheore54b__P,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.32/1.64        ( ( eoutM @ P @ M @ E )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.32/1.64                  & ( member @ secrecy_chanID @ Ch2 @ M ) )
% 0.32/1.64             => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_162_TBtheorem5b__PQ,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( ( eoutM @ P @ M @ E )
% 0.32/1.64          | ( eoutM @ Q @ M @ E ) )
% 0.32/1.64       => ( ( ( subcomponents @ PQ )
% 0.32/1.64            = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64         => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64           => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                  ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.32/1.64                    | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.32/1.64                  & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/1.64                  & ( exprChannel @ Ch2 @ E )
% 0.32/1.64                  & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64             => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_163_TBtheorem5b__notP1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.32/1.64        ( ( eoutM @ P @ M @ E )
% 0.32/1.64       => ( ~ ( eoutM @ Q @ M @ E )
% 0.32/1.64         => ( ( ( subcomponents @ PQ )
% 0.32/1.64              = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64           => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64             => ( ? [Ch2: secrecy_chanID] :
% 0.32/1.64                    ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ M )
% 0.32/1.64                    & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.32/1.64               => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_164_correctCompositionOut__prop1,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64         => ( ( member @ secrecy_chanID @ X3 @ ( out @ PQ ) )
% 0.32/1.64           => ( ( member @ secrecy_chanID @ X3 @ ( out @ P ) )
% 0.32/1.64              | ( member @ secrecy_chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_165_outStream__def,axiom,
% 0.32/1.64      ( outStream
% 0.32/1.64      = ( ^ [X2: secrecy_specID] :
% 0.32/1.64            ( ^ [Y: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y = Z )
% 0.32/1.64            @ ( out @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_166_TBtheorem5b__notPQ,axiom,
% 0.32/1.64      ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.32/1.64        ( ( ( subcomponents @ PQ )
% 0.32/1.64          = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.32/1.64       => ( ( correc990227761ionOut @ PQ )
% 0.32/1.64         => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.32/1.64           => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.32/1.64             => ( ( M
% 0.32/1.64                  = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.32/1.64               => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                      ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.32/1.64                     => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64                 => ( ! [X4: secrecy_chanID] :
% 0.32/1.64                        ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.32/1.64                       => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.32/1.64                   => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_167_insert__subsetI,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A,X5: set @ A] :
% 0.32/1.64        ( ( member @ A @ X3 @ A3 )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ X5 @ A3 )
% 0.32/1.64         => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X5 ) @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_168_UnCI,axiom,
% 0.32/1.64      ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.32/1.64        ( ( ~ ( member @ A @ C @ B )
% 0.32/1.64         => ( member @ A @ C @ A3 ) )
% 0.32/1.64       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_169_Un__iff,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64        = ( ( member @ A @ C @ A3 )
% 0.32/1.64          | ( member @ A @ C @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_170_Un__empty,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/1.64          = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64        = ( ( A3
% 0.32/1.64            = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          & ( B
% 0.32/1.64            = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_171_Un__insert__left,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,B: set @ A,C4: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/1.64        = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_172_Un__insert__right,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,A2: A,B: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/1.64        = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_173_Un__subset__iff,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.32/1.64        = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/1.64          & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_174_Un__empty__left,axiom,
% 0.32/1.64      ! [A: $tType,B: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 0.32/1.64        = B ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_175_Un__empty__right,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64        = A3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_176_subset__Un__eq,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) )
% 0.32/1.64        = ( ^ [A4: set @ A,B7: set @ A] :
% 0.32/1.64              ( ( sup_sup @ ( set @ A ) @ A4 @ B7 )
% 0.32/1.64              = B7 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_177_subset__UnE,axiom,
% 0.32/1.64      ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64       => ~ ! [A7: set @ A] :
% 0.32/1.64              ( ( ord_less_eq @ ( set @ A ) @ A7 @ A3 )
% 0.32/1.64             => ! [B8: set @ A] :
% 0.32/1.64                  ( ( ord_less_eq @ ( set @ A ) @ B8 @ B )
% 0.32/1.64                 => ( C4
% 0.32/1.64                   != ( sup_sup @ ( set @ A ) @ A7 @ B8 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_178_Un__absorb2,axiom,
% 0.32/1.64      ! [A: $tType,B: set @ A,A3: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.32/1.64       => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/1.64          = A3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_179_Un__absorb1,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.32/1.64       => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/1.64          = B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_180_Un__upper2,axiom,
% 0.32/1.64      ! [A: $tType,B: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_181_Un__upper1,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_182_Un__least,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.32/1.64         => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_183_Un__mono,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.32/1.64       => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 0.32/1.64         => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_184_ineM__Un1,axiom,
% 0.32/1.64      ! [P: secrecy_specID,A3: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 0.32/1.64        ( ( ineM @ P @ A3 @ E )
% 0.32/1.64       => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A3 @ B ) @ E ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_185_UnE,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64       => ( ~ ( member @ A @ C @ A3 )
% 0.32/1.64         => ( member @ A @ C @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_186_UnI1,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ A3 )
% 0.32/1.64       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_187_UnI2,axiom,
% 0.32/1.64      ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ B )
% 0.32/1.64       => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_188_bex__Un,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.32/1.64        ( ( ? [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64              & ( P @ X2 ) ) )
% 0.32/1.64        = ( ? [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ A3 )
% 0.32/1.64              & ( P @ X2 ) )
% 0.32/1.64          | ? [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ B )
% 0.32/1.64              & ( P @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_189_ball__Un,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.32/1.64        ( ( ! [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64             => ( P @ X2 ) ) )
% 0.32/1.64        = ( ! [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ A3 )
% 0.32/1.64             => ( P @ X2 ) )
% 0.32/1.64          & ! [X2: A] :
% 0.32/1.64              ( ( member @ A @ X2 @ B )
% 0.32/1.64             => ( P @ X2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_190_Un__assoc,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.32/1.64        = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_191_Un__absorb,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.32/1.64        = A3 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_192_Un__commute,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) )
% 0.32/1.64        = ( ^ [A4: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_193_Un__left__absorb,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64        = ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_194_Un__left__commute,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 0.32/1.64        = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_195_singleton__Un__iff,axiom,
% 0.32/1.64      ! [A: $tType,X3: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64          = ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64        = ( ( ( A3
% 0.32/1.64              = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/1.64          | ( ( A3
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64          | ( ( A3
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_196_Un__singleton__iff,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A,X3: A] :
% 0.32/1.64        ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.32/1.64          = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64        = ( ( ( A3
% 0.32/1.64              = ( bot_bot @ ( set @ A ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/1.64          | ( ( A3
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64          | ( ( A3
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.32/1.64            & ( B
% 0.32/1.64              = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_197_insert__is__Un,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( insert @ A )
% 0.32/1.64        = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_198_subset__emptyI,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A] :
% 0.32/1.64        ( ! [X4: A] :
% 0.32/1.64            ~ ( member @ A @ X4 @ A3 )
% 0.32/1.64       => ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_199_sup__bot_Oright__neutral,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [A2: A] :
% 0.32/1.64            ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.32/1.64            = A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_200_sup__bot_Oneutr__eq__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [A2: A,B2: A] :
% 0.32/1.64            ( ( ( bot_bot @ A )
% 0.32/1.64              = ( sup_sup @ A @ A2 @ B2 ) )
% 0.32/1.64            = ( ( A2
% 0.32/1.64                = ( bot_bot @ A ) )
% 0.32/1.64              & ( B2
% 0.32/1.64                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_201_sup__bot_Oleft__neutral,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [A2: A] :
% 0.32/1.64            ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.32/1.64            = A2 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_202_le__sup__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ ( sup_sup @ A @ X3 @ Y3 ) @ Z2 )
% 0.32/1.64            = ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.32/1.64              & ( ord_less_eq @ A @ Y3 @ Z2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_203_sup_Obounded__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,C: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 0.32/1.64            = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64              & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_204_sup__bot__left,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [X3: A] :
% 0.32/1.64            ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 0.32/1.64            = X3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_205_sup__bot__right,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [X3: A] :
% 0.32/1.64            ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 0.32/1.64            = X3 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_206_bot__eq__sup__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ( bot_bot @ A )
% 0.32/1.64              = ( sup_sup @ A @ X3 @ Y3 ) )
% 0.32/1.64            = ( ( X3
% 0.32/1.64                = ( bot_bot @ A ) )
% 0.32/1.64              & ( Y3
% 0.32/1.64                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_207_sup__eq__bot__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/1.64              = ( bot_bot @ A ) )
% 0.32/1.64            = ( ( X3
% 0.32/1.64                = ( bot_bot @ A ) )
% 0.32/1.64              & ( Y3
% 0.32/1.64                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_208_sup__bot_Oeq__neutr__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounde1808546759up_bot @ A )
% 0.32/1.64       => ! [A2: A,B2: A] :
% 0.32/1.64            ( ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/1.64              = ( bot_bot @ A ) )
% 0.32/1.64            = ( ( A2
% 0.32/1.64                = ( bot_bot @ A ) )
% 0.32/1.64              & ( B2
% 0.32/1.64                = ( bot_bot @ A ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_209_inf__sup__ord_I4_J,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( lattice @ A )
% 0.32/1.64       => ! [Y3: A,X3: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_210_inf__sup__ord_I3_J,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( lattice @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_211_le__supE,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,B2: A,X3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X3 )
% 0.32/1.64           => ~ ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.32/1.64               => ~ ( ord_less_eq @ A @ B2 @ X3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_212_le__supI,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,X3: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ B2 @ X3 )
% 0.32/1.64             => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_213_sup__ge1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] : ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_214_sup__ge2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [Y3: A,X3: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X3 @ Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_215_le__supI1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [X3: A,A2: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ A2 )
% 0.32/1.64           => ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_216_le__supI2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [X3: A,B2: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ B2 )
% 0.32/1.64           => ( ord_less_eq @ A @ X3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_217_sup_Omono,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [C: A,A2: A,D: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ D @ B2 )
% 0.32/1.64             => ( ord_less_eq @ A @ ( sup_sup @ A @ C @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_218_sup__mono,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,C: A,B2: A,D: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ C )
% 0.32/1.64           => ( ( ord_less_eq @ A @ B2 @ D )
% 0.32/1.64             => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C @ D ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_219_sup__least,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [Y3: A,X3: A,Z2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.32/1.64             => ( ord_less_eq @ A @ ( sup_sup @ A @ Y3 @ Z2 ) @ X3 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_220_le__iff__sup,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ( ( ord_less_eq @ A )
% 0.32/1.64          = ( ^ [X2: A,Y4: A] :
% 0.32/1.64                ( ( sup_sup @ A @ X2 @ Y4 )
% 0.32/1.64                = Y4 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_221_sup_OorderE,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64           => ( A2
% 0.32/1.64              = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_222_sup_OorderI,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,B2: A] :
% 0.32/1.64            ( ( A2
% 0.32/1.64              = ( sup_sup @ A @ A2 @ B2 ) )
% 0.32/1.64           => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_223_sup__unique,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [F: A > A > A,X3: A,Y3: A] :
% 0.32/1.64            ( ! [X4: A,Y2: A] : ( ord_less_eq @ A @ X4 @ ( F @ X4 @ Y2 ) )
% 0.32/1.64           => ( ! [X4: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X4 @ Y2 ) )
% 0.32/1.64             => ( ! [X4: A,Y2: A,Z3: A] :
% 0.32/1.64                    ( ( ord_less_eq @ A @ Y2 @ X4 )
% 0.32/1.64                   => ( ( ord_less_eq @ A @ Z3 @ X4 )
% 0.32/1.64                     => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X4 ) ) )
% 0.32/1.64               => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/1.64                  = ( F @ X3 @ Y3 ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_224_sup_Oabsorb1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64           => ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/1.64              = A2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_225_sup_Oabsorb2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64           => ( ( sup_sup @ A @ A2 @ B2 )
% 0.32/1.64              = B2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_226_sup__absorb1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [Y3: A,X3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.32/1.64           => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/1.64              = X3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_227_sup__absorb2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64           => ( ( sup_sup @ A @ X3 @ Y3 )
% 0.32/1.64              = Y3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_228_sup_OboundedE,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,C: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 )
% 0.32/1.64           => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64               => ~ ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_229_sup_OboundedI,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,A2: A,C: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.64           => ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/1.64             => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C ) @ A2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_230_sup_Oorder__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ( ( ord_less_eq @ A )
% 0.32/1.64          = ( ^ [B5: A,A5: A] :
% 0.32/1.64                ( A5
% 0.32/1.64                = ( sup_sup @ A @ A5 @ B5 ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_231_sup_Ocobounded1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_232_sup_Ocobounded2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_233_sup_Oabsorb__iff1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ( ( ord_less_eq @ A )
% 0.32/1.64          = ( ^ [B5: A,A5: A] :
% 0.32/1.64                ( ( sup_sup @ A @ A5 @ B5 )
% 0.32/1.64                = A5 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_234_sup_Oabsorb__iff2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ( ( ord_less_eq @ A )
% 0.32/1.64          = ( ^ [A5: A,B5: A] :
% 0.32/1.64                ( ( sup_sup @ A @ A5 @ B5 )
% 0.32/1.64                = B5 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_235_sup_OcoboundedI1,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [C: A,A2: A,B2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ C @ A2 )
% 0.32/1.64           => ( ord_less_eq @ A @ C @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_236_sup_OcoboundedI2,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A )
% 0.32/1.64       => ! [C: A,B2: A,A2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ C @ B2 )
% 0.32/1.64           => ( ord_less_eq @ A @ C @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_237_correctInOutLoc__def,axiom,
% 0.32/1.64      ( correctInOutLoc
% 0.32/1.64      = ( ^ [X2: secrecy_specID] :
% 0.32/1.64            ( ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( ins @ X2 ) @ ( out @ X2 ) )
% 0.32/1.64              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64            & ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( ins @ X2 ) @ ( loc @ X2 ) )
% 0.32/1.64              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.32/1.64            & ( ( inf_inf @ ( set @ secrecy_chanID ) @ ( loc @ X2 ) @ ( out @ X2 ) )
% 0.32/1.64              = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_238_subset__Compl__singleton,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B2: A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( uminus_uminus @ ( set @ A ) @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.32/1.64        = ( ~ ( member @ A @ B2 @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_239_IntI,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ A3 )
% 0.32/1.64       => ( ( member @ A @ C @ B )
% 0.32/1.64         => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_240_Int__iff,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64        = ( ( member @ A @ C @ A3 )
% 0.32/1.64          & ( member @ A @ C @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_241_ComplI,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ C @ A3 )
% 0.32/1.64       => ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_242_Compl__iff,axiom,
% 0.32/1.64      ! [A: $tType,C: A,A3: set @ A] :
% 0.32/1.64        ( ( member @ A @ C @ ( uminus_uminus @ ( set @ A ) @ A3 ) )
% 0.32/1.64        = ( ~ ( member @ A @ C @ A3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_243_Compl__eq__Compl__iff,axiom,
% 0.32/1.64      ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ( uminus_uminus @ ( set @ A ) @ A3 )
% 0.32/1.64          = ( uminus_uminus @ ( set @ A ) @ B ) )
% 0.32/1.64        = ( A3 = B ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_244_compl__le__compl__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( boolean_algebra @ A )
% 0.32/1.64       => ! [X3: A,Y3: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X3 ) @ ( uminus_uminus @ A @ Y3 ) )
% 0.32/1.64            = ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_245_le__inf__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_inf @ A )
% 0.32/1.64       => ! [X3: A,Y3: A,Z2: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ X3 @ ( inf_inf @ A @ Y3 @ Z2 ) )
% 0.32/1.64            = ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/1.64              & ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_246_inf_Obounded__iff,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( semilattice_inf @ A )
% 0.32/1.64       => ! [A2: A,B2: A,C: A] :
% 0.32/1.64            ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.32/1.64            = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.64              & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_247_inf__bot__left,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounded_lattice_bot @ A )
% 0.32/1.64       => ! [X3: A] :
% 0.32/1.64            ( ( inf_inf @ A @ ( bot_bot @ A ) @ X3 )
% 0.32/1.64            = ( bot_bot @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_248_inf__bot__right,axiom,
% 0.32/1.64      ! [A: $tType] :
% 0.32/1.64        ( ( bounded_lattice_bot @ A )
% 0.32/1.64       => ! [X3: A] :
% 0.32/1.64            ( ( inf_inf @ A @ X3 @ ( bot_bot @ A ) )
% 0.32/1.64            = ( bot_bot @ A ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_249_Int__insert__left__if0,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,C4: set @ A,B: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ A2 @ C4 )
% 0.32/1.64       => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/1.64          = ( inf_inf @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_250_Int__insert__left__if1,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,C4: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ C4 )
% 0.32/1.64       => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.32/1.64          = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B @ C4 ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_251_insert__inter__insert,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A3 ) @ ( insert @ A @ A2 @ B ) )
% 0.32/1.64        = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_252_Int__insert__right__if0,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ~ ( member @ A @ A2 @ A3 )
% 0.32/1.64       => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/1.64          = ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_253_Int__insert__right__if1,axiom,
% 0.32/1.64      ! [A: $tType,A2: A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( member @ A @ A2 @ A3 )
% 0.32/1.64       => ( ( inf_inf @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.32/1.64          = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_254_Int__subset__iff,axiom,
% 0.32/1.64      ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 0.32/1.64        ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A3 @ B ) )
% 0.32/1.64        = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A3 )
% 0.32/1.64          & ( ord_less_eq @ ( set @ A ) @ C4 @ B ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(fact_255_Int__Un__eq_I4_J,axiom,
% 0.32/1.64      ! [A: $tType,T2: set @ A,S: set @ A] :
% 0.32/1.64        ( ( sup_sup @ ( set @ A ) @ T2 @ ( inf_inf @ ( set @ A ) @ S @ T2 ) )
% 0.32/1.64        = T2 ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.32/1.64      bounded_lattice @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.32/1.64      ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( bounded_lattice @ A9 )
% 0.32/1.64       => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( bounded_lattice @ A9 )
% 0.32/1.64       => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( bounded_lattice @ A9 )
% 0.32/1.64       => ( bounded_lattice_bot @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( semilattice_sup @ A9 )
% 0.32/1.64       => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( semilattice_inf @ A9 )
% 0.32/1.64       => ( semilattice_inf @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( boolean_algebra @ A9 )
% 0.32/1.64       => ( boolean_algebra @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( order_bot @ A9 )
% 0.32/1.64       => ( order_bot @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( preorder @ A9 )
% 0.32/1.64       => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Lattices_Olattice,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( lattice @ A9 )
% 0.32/1.64       => ( lattice @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( order @ A9 )
% 0.32/1.64       => ( order @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( ord @ A9 )
% 0.32/1.64       => ( ord @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_fun___Orderings_Obot,axiom,
% 0.32/1.64      ! [A8: $tType,A9: $tType] :
% 0.32/1.64        ( ( bot @ A9 )
% 0.32/1.64       => ( bot @ ( A8 > A9 ) ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.32/1.64      semilattice_sup @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_4,axiom,
% 0.32/1.64      semilattice_inf @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Oorder__bot_5,axiom,
% 0.32/1.64      order_bot @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Opreorder_6,axiom,
% 0.32/1.64      preorder @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/1.64      linorder @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Lattices_Olattice_7,axiom,
% 0.32/1.64      lattice @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Oorder_8,axiom,
% 0.32/1.64      order @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Oord_9,axiom,
% 0.32/1.64      ord @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Nat_Onat___Orderings_Obot_10,axiom,
% 0.32/1.64      bot @ nat ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_11,axiom,
% 0.32/1.64      ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_12,axiom,
% 0.32/1.64      ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Osemilattice__sup_13,axiom,
% 0.32/1.64      ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Osemilattice__inf_14,axiom,
% 0.32/1.64      ! [A8: $tType] : ( semilattice_inf @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Oboolean__algebra_15,axiom,
% 0.32/1.64      ! [A8: $tType] : ( boolean_algebra @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Orderings_Oorder__bot_16,axiom,
% 0.32/1.64      ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Orderings_Opreorder_17,axiom,
% 0.32/1.64      ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Lattices_Olattice_18,axiom,
% 0.32/1.64      ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Orderings_Oorder_19,axiom,
% 0.32/1.64      ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Orderings_Oord_20,axiom,
% 0.32/1.64      ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_Set_Oset___Orderings_Obot_21,axiom,
% 0.32/1.64      ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_22,axiom,
% 0.32/1.64      bounde1808546759up_bot @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_23,axiom,
% 0.32/1.64      bounded_lattice_bot @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_24,axiom,
% 0.32/1.64      semilattice_sup @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_25,axiom,
% 0.32/1.64      semilattice_inf @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_26,axiom,
% 0.32/1.64      boolean_algebra @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Oorder__bot_27,axiom,
% 0.32/1.64      order_bot @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Opreorder_28,axiom,
% 0.32/1.64      preorder @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Olinorder_29,axiom,
% 0.32/1.64      linorder @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Lattices_Olattice_30,axiom,
% 0.32/1.64      lattice @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Oorder_31,axiom,
% 0.32/1.64      order @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Oord_32,axiom,
% 0.32/1.64      ord @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(tcon_HOL_Obool___Orderings_Obot_33,axiom,
% 0.32/1.64      bot @ $o ).
% 0.32/1.64  
% 0.32/1.64  thf(conj_0,conjecture,
% 0.32/1.64      member @ secrecy_chanID @ ch @ ( loc @ pq ) ).
% 0.32/1.64  ------------------------
% 0.32/1.67  % (8019)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/183Mi)
% 0.32/1.67  % (8021)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_7835 for (2999ds/27Mi)
% 0.32/1.67  % (8025)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/18Mi)
% 0.32/1.67  % (8022)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/2Mi)
% 0.32/1.67  % (8022)Instruction limit reached!
% 0.32/1.67  % (8022)------------------------------
% 0.32/1.67  % (8022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.67  % (8022)Termination reason: Unknown
% 0.32/1.67  % (8022)Termination phase: shuffling
% 0.32/1.67  
% 0.32/1.67  % (8020)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_7835 for (2999ds/4Mi)
% 0.32/1.67  % (8022)Memory used [KB]: 1279
% 0.32/1.67  % (8022)Time elapsed: 0.003 s
% 0.32/1.67  % (8022)Instructions burned: 3 (million)
% 0.32/1.67  % (8022)------------------------------
% 0.32/1.67  % (8022)------------------------------
% 0.32/1.67  % (8023)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_7835 for (2999ds/2Mi)
% 0.32/1.67  % (8023)Instruction limit reached!
% 0.32/1.67  % (8023)------------------------------
% 0.32/1.67  % (8023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.67  % (8023)Termination reason: Unknown
% 0.32/1.67  % (8023)Termination phase: shuffling
% 0.32/1.67  
% 0.32/1.67  % (8023)Memory used [KB]: 1279
% 0.32/1.67  % (8023)Time elapsed: 0.003 s
% 0.32/1.67  % (8023)Instructions burned: 2 (million)
% 0.32/1.67  % (8023)------------------------------
% 0.32/1.67  % (8023)------------------------------
% 0.32/1.67  % (8020)Instruction limit reached!
% 0.32/1.67  % (8020)------------------------------
% 0.32/1.67  % (8020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.67  % (8020)Termination reason: Unknown
% 0.32/1.67  % (8020)Termination phase: shuffling
% 0.32/1.67  
% 0.32/1.67  % (8020)Memory used [KB]: 1407
% 0.32/1.67  % (8020)Time elapsed: 0.004 s
% 0.32/1.67  % (8020)Instructions burned: 4 (million)
% 0.32/1.67  % (8020)------------------------------
% 0.32/1.67  % (8020)------------------------------
% 0.32/1.68  % (8025)Instruction limit reached!
% 0.32/1.68  % (8025)------------------------------
% 0.32/1.68  % (8025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.68  % (8025)Termination reason: Unknown
% 0.32/1.68  % (8025)Termination phase: shuffling
% 0.32/1.68  
% 0.32/1.68  % (8025)Memory used [KB]: 1663
% 0.32/1.68  % (8025)Time elapsed: 0.010 s
% 0.32/1.68  % (8025)Instructions burned: 18 (million)
% 0.32/1.68  % (8025)------------------------------
% 0.32/1.68  % (8025)------------------------------
% 0.32/1.68  % (8024)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_7835 for (2999ds/275Mi)
% 0.32/1.68  % (8021)Instruction limit reached!
% 0.32/1.68  % (8021)------------------------------
% 0.32/1.68  % (8021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.68  % (8021)Termination reason: Unknown
% 0.32/1.68  % (8021)Termination phase: Property scanning
% 0.32/1.68  
% 0.32/1.68  % (8021)Memory used [KB]: 1791
% 0.32/1.68  % (8021)Time elapsed: 0.015 s
% 0.32/1.68  % (8021)Instructions burned: 27 (million)
% 0.32/1.68  % (8021)------------------------------
% 0.32/1.68  % (8021)------------------------------
% 0.32/1.69  % (8031)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_7835 for (2999ds/3Mi)
% 0.32/1.69  % (8027)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/3Mi)
% 0.32/1.69  % (8031)Instruction limit reached!
% 0.32/1.69  % (8031)------------------------------
% 0.32/1.69  % (8031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.69  % (8031)Termination reason: Unknown
% 0.32/1.69  % (8031)Termination phase: shuffling
% 0.32/1.69  
% 0.32/1.69  % (8031)Memory used [KB]: 1407
% 0.32/1.69  % (8031)Time elapsed: 0.002 s
% 0.32/1.69  % (8031)Instructions burned: 3 (million)
% 0.32/1.69  % (8031)------------------------------
% 0.32/1.69  % (8031)------------------------------
% 0.32/1.69  % (8028)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_7835 for (2999ds/37Mi)
% 0.32/1.69  % (8027)Instruction limit reached!
% 0.32/1.69  % (8027)------------------------------
% 0.32/1.69  % (8027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.69  % (8027)Termination reason: Unknown
% 0.32/1.69  % (8027)Termination phase: shuffling
% 0.32/1.69  
% 0.32/1.69  % (8027)Memory used [KB]: 1407
% 0.32/1.69  % (8027)Time elapsed: 0.003 s
% 0.32/1.69  % (8027)Instructions burned: 3 (million)
% 0.32/1.69  % (8027)------------------------------
% 0.32/1.69  % (8027)------------------------------
% 0.32/1.69  % (8029)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_7835 for (2999ds/15Mi)
% 2.83/1.70  % (8029)Instruction limit reached!
% 2.83/1.70  % (8029)------------------------------
% 2.83/1.70  % (8029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.70  % (8029)Termination reason: Unknown
% 2.83/1.70  % (8029)Termination phase: shuffling
% 2.83/1.70  
% 2.83/1.70  % (8029)Memory used [KB]: 1535
% 2.83/1.70  % (8029)Time elapsed: 0.009 s
% 2.83/1.70  % (8029)Instructions burned: 15 (million)
% 2.83/1.70  % (8029)------------------------------
% 2.83/1.70  % (8029)------------------------------
% 2.83/1.70  % (8033)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/7Mi)
% 2.83/1.70  % (8032)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_7835 for (2999ds/1041Mi)
% 2.83/1.70  % (8033)Instruction limit reached!
% 2.83/1.70  % (8033)------------------------------
% 2.83/1.70  % (8033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.70  % (8033)Termination reason: Unknown
% 2.83/1.70  % (8033)Termination phase: shuffling
% 2.83/1.70  
% 2.83/1.70  % (8033)Memory used [KB]: 1535
% 2.83/1.70  % (8033)Time elapsed: 0.004 s
% 2.83/1.70  % (8033)Instructions burned: 9 (million)
% 2.83/1.70  % (8033)------------------------------
% 2.83/1.70  % (8033)------------------------------
% 2.83/1.71  % (8024)Refutation not found, incomplete strategy
% 2.83/1.71  % (8024)------------------------------
% 2.83/1.71  % (8024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.71  % (8024)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.71  
% 2.83/1.71  
% 2.83/1.71  % (8024)Memory used [KB]: 6268
% 2.83/1.71  % (8024)Time elapsed: 0.027 s
% 2.83/1.71  % (8024)Instructions burned: 45 (million)
% 2.83/1.71  % (8024)------------------------------
% 2.83/1.71  % (8024)------------------------------
% 2.83/1.71  % (8034)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/16Mi)
% 2.83/1.71  % (8028)Instruction limit reached!
% 2.83/1.71  % (8028)------------------------------
% 2.83/1.71  % (8028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.71  % (8028)Termination reason: Unknown
% 2.83/1.71  % (8028)Termination phase: shuffling
% 2.83/1.71  
% 2.83/1.71  % (8028)Memory used [KB]: 2046
% 2.83/1.71  % (8028)Time elapsed: 0.020 s
% 2.83/1.71  % (8028)Instructions burned: 38 (million)
% 2.83/1.71  % (8028)------------------------------
% 2.83/1.71  % (8028)------------------------------
% 2.83/1.71  % (8036)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_7835 for (2999ds/3Mi)
% 2.83/1.71  % (8036)Instruction limit reached!
% 2.83/1.71  % (8036)------------------------------
% 2.83/1.71  % (8036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.71  % (8036)Termination reason: Unknown
% 2.83/1.71  % (8036)Termination phase: shuffling
% 2.83/1.71  
% 2.83/1.71  % (8036)Memory used [KB]: 1407
% 2.83/1.71  % (8036)Time elapsed: 0.002 s
% 2.83/1.71  % (8036)Instructions burned: 3 (million)
% 2.83/1.71  % (8036)------------------------------
% 2.83/1.71  % (8036)------------------------------
% 2.83/1.72  % (8035)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_7835 for (2999ds/3Mi)
% 2.83/1.72  % (8035)Instruction limit reached!
% 2.83/1.72  % (8035)------------------------------
% 2.83/1.72  % (8035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.72  % (8035)Termination reason: Unknown
% 2.83/1.72  % (8035)Termination phase: shuffling
% 2.83/1.72  
% 2.83/1.72  % (8035)Memory used [KB]: 1407
% 2.83/1.72  % (8035)Time elapsed: 0.003 s
% 2.83/1.72  % (8035)Instructions burned: 3 (million)
% 2.83/1.72  % (8035)------------------------------
% 2.83/1.72  % (8035)------------------------------
% 2.83/1.72  % (8034)Instruction limit reached!
% 2.83/1.72  % (8034)------------------------------
% 2.83/1.72  % (8034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.72  % (8034)Termination reason: Unknown
% 2.83/1.72  % (8034)Termination phase: shuffling
% 2.83/1.72  
% 2.83/1.72  % (8034)Memory used [KB]: 1663
% 2.83/1.72  % (8034)Time elapsed: 0.011 s
% 2.83/1.72  % (8034)Instructions burned: 17 (million)
% 2.83/1.72  % (8034)------------------------------
% 2.83/1.72  % (8034)------------------------------
% 2.83/1.72  % (8039)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/4Mi)
% 2.83/1.72  % (8039)Instruction limit reached!
% 2.83/1.72  % (8039)------------------------------
% 2.83/1.72  % (8039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.72  % (8039)Termination reason: Unknown
% 2.83/1.72  % (8039)Termination phase: shuffling
% 2.83/1.72  
% 2.83/1.72  % (8039)Memory used [KB]: 1407
% 2.83/1.72  % (8039)Time elapsed: 0.003 s
% 2.83/1.72  % (8039)Instructions burned: 6 (million)
% 2.83/1.72  % (8039)------------------------------
% 2.83/1.72  % (8039)------------------------------
% 2.83/1.72  % (8037)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/7Mi)
% 2.83/1.73  % (8038)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/3Mi)
% 2.83/1.73  % (8038)Instruction limit reached!
% 2.83/1.73  % (8038)------------------------------
% 2.83/1.73  % (8038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.73  % (8038)Termination reason: Unknown
% 2.83/1.73  % (8038)Termination phase: shuffling
% 2.83/1.73  
% 2.83/1.73  % (8038)Memory used [KB]: 1407
% 2.83/1.73  % (8038)Time elapsed: 0.003 s
% 2.83/1.73  % (8038)Instructions burned: 4 (million)
% 2.83/1.73  % (8038)------------------------------
% 2.83/1.73  % (8038)------------------------------
% 2.83/1.73  % (8037)Instruction limit reached!
% 2.83/1.73  % (8037)------------------------------
% 2.83/1.73  % (8037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.73  % (8037)Termination reason: Unknown
% 2.83/1.73  % (8037)Termination phase: shuffling
% 2.83/1.73  
% 2.83/1.73  % (8037)Memory used [KB]: 1535
% 2.83/1.73  % (8037)Time elapsed: 0.006 s
% 2.83/1.73  % (8037)Instructions burned: 8 (million)
% 2.83/1.73  % (8037)------------------------------
% 2.83/1.73  % (8037)------------------------------
% 2.83/1.73  % (8040)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/18Mi)
% 2.83/1.73  % (8042)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/6Mi)
% 2.83/1.73  % (8041)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/710Mi)
% 2.83/1.74  % (8042)Instruction limit reached!
% 2.83/1.74  % (8042)------------------------------
% 2.83/1.74  % (8042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74  % (8042)Termination reason: Unknown
% 2.83/1.74  % (8042)Termination phase: shuffling
% 2.83/1.74  
% 2.83/1.74  % (8042)Memory used [KB]: 1407
% 2.83/1.74  % (8042)Time elapsed: 0.003 s
% 2.83/1.74  % (8042)Instructions burned: 6 (million)
% 2.83/1.74  % (8042)------------------------------
% 2.83/1.74  % (8042)------------------------------
% 2.83/1.74  % (8019)Instruction limit reached!
% 2.83/1.74  % (8019)------------------------------
% 2.83/1.74  % (8019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74  % (8019)Termination reason: Unknown
% 2.83/1.74  % (8019)Termination phase: Saturation
% 2.83/1.74  
% 2.83/1.74  % (8019)Memory used [KB]: 7036
% 2.83/1.74  % (8019)Time elapsed: 0.078 s
% 2.83/1.74  % (8019)Instructions burned: 184 (million)
% 2.83/1.74  % (8019)------------------------------
% 2.83/1.74  % (8019)------------------------------
% 2.83/1.74  % (8040)Instruction limit reached!
% 2.83/1.74  % (8040)------------------------------
% 2.83/1.74  % (8040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74  % (8040)Termination reason: Unknown
% 2.83/1.74  % (8040)Termination phase: shuffling
% 2.83/1.74  
% 2.83/1.74  % (8040)Memory used [KB]: 1663
% 2.83/1.74  % (8040)Time elapsed: 0.011 s
% 2.83/1.74  % (8040)Instructions burned: 19 (million)
% 2.83/1.74  % (8040)------------------------------
% 2.83/1.74  % (8040)------------------------------
% 2.83/1.74  % (8043)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_7835 for (2999ds/902Mi)
% 2.83/1.75  % (8046)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/5Mi)
% 2.83/1.75  % (8046)Instruction limit reached!
% 2.83/1.75  % (8046)------------------------------
% 2.83/1.75  % (8046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.75  % (8046)Termination reason: Unknown
% 2.83/1.75  % (8046)Termination phase: shuffling
% 2.83/1.75  
% 2.83/1.75  % (8046)Memory used [KB]: 1407
% 2.83/1.75  % (8046)Time elapsed: 0.004 s
% 2.83/1.75  % (8046)Instructions burned: 5 (million)
% 2.83/1.75  % (8046)------------------------------
% 2.83/1.75  % (8046)------------------------------
% 2.83/1.75  % (8044)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_7835 for (2999ds/21Mi)
% 2.83/1.76  % (8049)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7835 for (2999ds/377Mi)
% 2.83/1.76  % (8048)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_7835 for (2999ds/6Mi)
% 2.83/1.76  % (8044)Instruction limit reached!
% 2.83/1.76  % (8044)------------------------------
% 2.83/1.76  % (8044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.76  % (8044)Termination reason: Unknown
% 2.83/1.76  % (8044)Termination phase: shuffling
% 2.83/1.76  
% 2.83/1.76  % (8044)Memory used [KB]: 1791
% 2.83/1.76  % (8044)Time elapsed: 0.011 s
% 2.83/1.76  % (8044)Instructions burned: 23 (million)
% 2.83/1.76  % (8044)------------------------------
% 2.83/1.76  % (8044)------------------------------
% 2.83/1.76  % (8048)Instruction limit reached!
% 2.83/1.76  % (8048)------------------------------
% 2.83/1.76  % (8048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.76  % (8048)Termination reason: Unknown
% 2.83/1.76  % (8048)Termination phase: shuffling
% 2.83/1.76  
% 2.83/1.76  % (8048)Memory used [KB]: 1407
% 2.83/1.76  % (8048)Time elapsed: 0.005 s
% 2.83/1.76  % (8048)Instructions burned: 7 (million)
% 2.83/1.76  % (8048)------------------------------
% 2.83/1.76  % (8048)------------------------------
% 2.83/1.77  % (8050)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_7835 for (2999ds/779Mi)
% 2.83/1.77  % (8052)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_7835 for (2999ds/19Mi)
% 2.83/1.78  % (8052)Instruction limit reached!
% 2.83/1.78  % (8052)------------------------------
% 2.83/1.78  % (8052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.78  % (8052)Termination reason: Unknown
% 2.83/1.78  % (8052)Termination phase: shuffling
% 2.83/1.78  
% 2.83/1.78  % (8052)Memory used [KB]: 1663
% 2.83/1.78  % (8052)Time elapsed: 0.009 s
% 2.83/1.78  % (8052)Instructions burned: 20 (million)
% 2.83/1.78  % (8054)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/879Mi)
% 2.83/1.78  % (8052)------------------------------
% 2.83/1.78  % (8052)------------------------------
% 2.83/1.79  % (8056)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/17Mi)
% 2.83/1.80  % (8056)Instruction limit reached!
% 2.83/1.80  % (8056)------------------------------
% 2.83/1.80  % (8056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.80  % (8056)Termination reason: Unknown
% 2.83/1.80  % (8056)Termination phase: shuffling
% 2.83/1.80  
% 2.83/1.80  % (8056)Memory used [KB]: 1663
% 2.83/1.80  % (8056)Time elapsed: 0.010 s
% 2.83/1.80  % (8056)Instructions burned: 17 (million)
% 2.83/1.80  % (8056)------------------------------
% 2.83/1.80  % (8056)------------------------------
% 2.83/1.81  % (8043)Refutation not found, incomplete strategy
% 2.83/1.81  % (8043)------------------------------
% 2.83/1.81  % (8043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.81  % (8043)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.81  
% 2.83/1.81  
% 2.83/1.81  % (8043)Memory used [KB]: 7036
% 2.83/1.81  % (8043)Time elapsed: 0.065 s
% 2.83/1.81  % (8043)Instructions burned: 131 (million)
% 2.83/1.81  % (8043)------------------------------
% 2.83/1.81  % (8043)------------------------------
% 2.83/1.82  % (8058)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/3Mi)
% 2.83/1.82  % (8058)Instruction limit reached!
% 2.83/1.82  % (8058)------------------------------
% 2.83/1.82  % (8058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.82  % (8058)Termination reason: Unknown
% 2.83/1.82  % (8058)Termination phase: shuffling
% 2.83/1.82  
% 2.83/1.82  % (8058)Memory used [KB]: 1407
% 2.83/1.82  % (8058)Time elapsed: 0.003 s
% 2.83/1.82  % (8058)Instructions burned: 3 (million)
% 2.83/1.82  % (8058)------------------------------
% 2.83/1.82  % (8058)------------------------------
% 2.83/1.82  % (8059)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/30Mi)
% 2.83/1.84  % (8061)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/127Mi)
% 2.83/1.84  % (8059)Instruction limit reached!
% 2.83/1.84  % (8059)------------------------------
% 2.83/1.84  % (8059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.84  % (8059)Termination reason: Unknown
% 2.83/1.84  % (8059)Termination phase: Property scanning
% 2.83/1.84  
% 2.83/1.84  % (8059)Memory used [KB]: 1918
% 2.83/1.84  % (8059)Time elapsed: 0.016 s
% 2.83/1.84  % (8059)Instructions burned: 30 (million)
% 2.83/1.84  % (8059)------------------------------
% 2.83/1.84  % (8059)------------------------------
% 2.83/1.85  % (8063)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7835 for (2998ds/100Mi)
% 2.83/1.90  % (8049)Instruction limit reached!
% 2.83/1.90  % (8049)------------------------------
% 2.83/1.90  % (8049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90  % (8049)Termination reason: Unknown
% 2.83/1.90  % (8061)Instruction limit reached!
% 2.83/1.90  % (8061)------------------------------
% 2.83/1.90  % (8061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90  % (8049)Termination phase: Saturation
% 2.83/1.90  
% 2.83/1.90  % (8061)Termination reason: Unknown
% 2.83/1.90  % (8049)Memory used [KB]: 7675
% 2.83/1.90  % (8061)Termination phase: Saturation
% 2.83/1.90  % (8049)Time elapsed: 0.138 s
% 2.83/1.90  
% 2.83/1.90  % (8049)Instructions burned: 378 (million)
% 2.83/1.90  % (8049)------------------------------
% 2.83/1.90  % (8049)------------------------------
% 2.83/1.90  % (8061)Memory used [KB]: 6780
% 2.83/1.90  % (8061)Time elapsed: 0.060 s
% 2.83/1.90  % (8061)Instructions burned: 127 (million)
% 2.83/1.90  % (8061)------------------------------
% 2.83/1.90  % (8061)------------------------------
% 2.83/1.90  % (8063)Instruction limit reached!
% 2.83/1.90  % (8063)------------------------------
% 2.83/1.90  % (8063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90  % (8063)Termination reason: Unknown
% 2.83/1.90  % (8063)Termination phase: Property scanning
% 2.83/1.90  
% 2.83/1.90  % (8063)Memory used [KB]: 2302
% 2.83/1.90  % (8063)Time elapsed: 0.047 s
% 2.83/1.90  % (8063)Instructions burned: 101 (million)
% 2.83/1.90  % (8063)------------------------------
% 2.83/1.90  % (8063)------------------------------
% 2.83/1.91  % (8066)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_7835 for (2997ds/3Mi)
% 2.83/1.91  % (8066)Instruction limit reached!
% 2.83/1.91  % (8066)------------------------------
% 2.83/1.91  % (8066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.91  % (8066)Termination reason: Unknown
% 2.83/1.91  % (8066)Termination phase: shuffling
% 2.83/1.91  
% 2.83/1.91  % (8066)Memory used [KB]: 1407
% 2.83/1.91  % (8066)Time elapsed: 0.003 s
% 2.83/1.91  % (8066)Instructions burned: 5 (million)
% 2.83/1.91  % (8066)------------------------------
% 2.83/1.91  % (8066)------------------------------
% 2.83/1.91  % (8067)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_7835 for (2997ds/20Mi)
% 2.83/1.92  % (8068)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_7835 for (2997ds/86Mi)
% 2.83/1.92  % (8067)Instruction limit reached!
% 2.83/1.92  % (8067)------------------------------
% 2.83/1.92  % (8067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.92  % (8067)Termination reason: Unknown
% 2.83/1.92  % (8067)Termination phase: shuffling
% 2.83/1.92  
% 2.83/1.92  % (8067)Memory used [KB]: 1663
% 2.83/1.92  % (8067)Time elapsed: 0.012 s
% 2.83/1.92  % (8067)Instructions burned: 21 (million)
% 2.83/1.92  % (8067)------------------------------
% 2.83/1.92  % (8067)------------------------------
% 2.83/1.92  % (8070)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_7835 for (2997ds/107Mi)
% 2.83/1.94  % (8071)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_7835 for (2997ds/39Mi)
% 2.83/1.96  % (8071)Instruction limit reached!
% 2.83/1.96  % (8071)------------------------------
% 2.83/1.96  % (8071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.96  % (8071)Termination reason: Unknown
% 2.83/1.96  % (8071)Termination phase: shuffling
% 2.83/1.96  
% 2.83/1.96  % (8071)Memory used [KB]: 2046
% 2.83/1.96  % (8071)Time elapsed: 0.020 s
% 2.83/1.96  % (8071)Instructions burned: 40 (million)
% 2.83/1.96  % (8071)------------------------------
% 2.83/1.96  % (8071)------------------------------
% 2.83/1.96  % (8068)Instruction limit reached!
% 2.83/1.96  % (8068)------------------------------
% 2.83/1.96  % (8068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.96  % (8068)Termination reason: Unknown
% 2.83/1.96  % (8068)Termination phase: Property scanning
% 2.83/1.96  
% 2.83/1.96  % (8068)Memory used [KB]: 2174
% 2.83/1.96  % (8068)Time elapsed: 0.042 s
% 2.83/1.96  % (8068)Instructions burned: 87 (million)
% 2.83/1.96  % (8068)------------------------------
% 2.83/1.96  % (8068)------------------------------
% 2.83/1.96  % (8070)Instruction limit reached!
% 2.83/1.96  % (8070)------------------------------
% 2.83/1.96  % (8070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.96  % (8070)Termination reason: Unknown
% 2.83/1.96  % (8070)Termination phase: Saturation
% 2.83/1.96  
% 2.83/1.96  % (8070)Memory used [KB]: 6652
% 2.83/1.96  % (8070)Time elapsed: 0.040 s
% 2.83/1.96  % (8070)Instructions burned: 109 (million)
% 2.83/1.96  % (8070)------------------------------
% 2.83/1.96  % (8070)------------------------------
% 2.83/1.97  % (8076)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_7835 for (2997ds/98Mi)
% 2.83/1.97  % (8074)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_7835 for (2997ds/448Mi)
% 2.83/1.98  % (8075)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_7835 for (2997ds/46Mi)
% 2.83/1.99  % (8075)Instruction limit reached!
% 2.83/1.99  % (8075)------------------------------
% 2.83/1.99  % (8075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.99  % (8075)Termination reason: Unknown
% 2.83/1.99  % (8075)Termination phase: SInE selection
% 2.83/1.99  
% 2.83/1.99  % (8075)Memory used [KB]: 1918
% 2.83/1.99  % (8075)Time elapsed: 0.017 s
% 2.83/1.99  % (8075)Instructions burned: 48 (million)
% 2.83/1.99  % (8075)------------------------------
% 2.83/1.99  % (8075)------------------------------
% 2.83/2.00  % (8080)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_7835 for (2996ds/507Mi)
% 2.83/2.01  % (8076)Instruction limit reached!
% 2.83/2.01  % (8076)------------------------------
% 2.83/2.01  % (8076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/2.01  % (8076)Termination reason: Unknown
% 2.83/2.01  % (8076)Termination phase: Property scanning
% 2.83/2.01  
% 2.83/2.01  % (8076)Memory used [KB]: 2302
% 2.83/2.01  % (8076)Time elapsed: 0.040 s
% 2.83/2.01  % (8076)Instructions burned: 98 (million)
% 2.83/2.01  % (8076)------------------------------
% 2.83/2.01  % (8076)------------------------------
% 5.30/2.03  % (8084)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_7835 for (2996ds/149Mi)
% 5.30/2.05  % (8041)Instruction limit reached!
% 5.30/2.05  % (8041)------------------------------
% 5.30/2.05  % (8041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.05  % (8041)Termination reason: Unknown
% 5.30/2.05  % (8041)Termination phase: Saturation
% 5.30/2.05  
% 5.30/2.05  % (8041)Memory used [KB]: 8187
% 5.30/2.05  % (8041)Time elapsed: 0.317 s
% 5.30/2.05  % (8041)Instructions burned: 711 (million)
% 5.30/2.05  % (8041)------------------------------
% 5.30/2.05  % (8041)------------------------------
% 5.30/2.07  % (8088)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7835 for (2996ds/39Mi)
% 5.30/2.08  % (8080)Refutation not found, incomplete strategy
% 5.30/2.08  % (8080)------------------------------
% 5.30/2.08  % (8080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.08  % (8080)Termination reason: Refutation not found, incomplete strategy
% 5.30/2.08  
% 5.30/2.08  
% 5.30/2.08  % (8080)Memory used [KB]: 7291
% 5.30/2.08  % (8080)Time elapsed: 0.078 s
% 5.30/2.08  % (8080)Instructions burned: 165 (million)
% 5.30/2.08  % (8080)------------------------------
% 5.30/2.08  % (8080)------------------------------
% 5.30/2.09  % (8088)Instruction limit reached!
% 5.30/2.09  % (8088)------------------------------
% 5.30/2.09  % (8088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.09  % (8088)Termination reason: Unknown
% 5.30/2.09  % (8088)Termination phase: Property scanning
% 5.30/2.09  
% 5.30/2.09  % (8088)Memory used [KB]: 1791
% 5.30/2.09  % (8088)Time elapsed: 0.021 s
% 5.30/2.09  % (8088)Instructions burned: 39 (million)
% 5.30/2.09  % (8088)------------------------------
% 5.30/2.09  % (8088)------------------------------
% 5.30/2.10  % (8091)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_7835 for (2995ds/6Mi)
% 5.30/2.10  % (8091)Instruction limit reached!
% 5.30/2.10  % (8091)------------------------------
% 5.30/2.10  % (8091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.10  % (8091)Termination reason: Unknown
% 5.30/2.10  % (8091)Termination phase: shuffling
% 5.30/2.10  
% 5.30/2.10  % (8091)Memory used [KB]: 1407
% 5.30/2.10  % (8091)Time elapsed: 0.005 s
% 5.30/2.10  % (8091)Instructions burned: 7 (million)
% 5.30/2.10  % (8091)------------------------------
% 5.30/2.10  % (8091)------------------------------
% 5.30/2.10  % (8084)Instruction limit reached!
% 5.30/2.10  % (8084)------------------------------
% 5.30/2.10  % (8084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.10  % (8084)Termination reason: Unknown
% 5.30/2.10  % (8084)Termination phase: Saturation
% 5.30/2.10  
% 5.30/2.10  % (8084)Memory used [KB]: 6780
% 5.30/2.10  % (8084)Time elapsed: 0.071 s
% 5.30/2.10  % (8084)Instructions burned: 149 (million)
% 5.30/2.10  % (8084)------------------------------
% 5.30/2.10  % (8084)------------------------------
% 5.30/2.10  % (8092)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_7835 for (2995ds/1087Mi)
% 5.30/2.11  % (8054)Refutation not found, non-redundant clauses discarded% (8054)------------------------------
% 5.30/2.11  % (8054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.11  % (8054)Termination reason: Refutation not found, non-redundant clauses discarded
% 5.30/2.11  
% 5.30/2.11  % (8054)Memory used [KB]: 7931
% 5.30/2.11  % (8054)Time elapsed: 0.331 s
% 5.30/2.11  % (8054)Instructions burned: 731 (million)
% 5.30/2.11  % (8054)------------------------------
% 5.30/2.11  % (8054)------------------------------
% 5.30/2.11  % (8095)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_7835 for (2995ds/44Mi)
% 5.30/2.12  % (8094)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7835 for (2995ds/47Mi)
% 5.30/2.12  % (8050)Instruction limit reached!
% 5.30/2.12  % (8050)------------------------------
% 5.30/2.12  % (8050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.30/2.12  % (8050)Termination reason: Unknown
% 5.30/2.12  % (8050)Termination phase: Saturation
% 5.30/2.12  
% 5.30/2.12  % (8050)Memory used [KB]: 7931
% 5.30/2.12  % (8050)Time elapsed: 0.353 s
% 5.30/2.12  % (8050)Instructions burned: 780 (million)
% 5.30/2.12  % (8050)------------------------------
% 5.30/2.12  % (8050)------------------------------
% 5.96/2.13  % (8100)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_7835 for (2995ds/432Mi)
% 5.96/2.13  % (8095)Instruction limit reached!
% 5.96/2.13  % (8095)------------------------------
% 5.96/2.13  % (8095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.13  % (8095)Termination reason: Unknown
% 5.96/2.13  % (8095)Termination phase: Property scanning
% 5.96/2.13  
% 5.96/2.13  % (8095)Memory used [KB]: 2174
% 5.96/2.13  % (8095)Time elapsed: 0.014 s
% 5.96/2.13  % (8095)Instructions burned: 47 (million)
% 5.96/2.13  % (8095)------------------------------
% 5.96/2.13  % (8095)------------------------------
% 5.96/2.13  % (8101)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7835 for (2995ds/62Mi)
% 5.96/2.14  % (8102)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_7835 for (2995ds/31Mi)
% 5.96/2.14  % (8094)Instruction limit reached!
% 5.96/2.14  % (8094)------------------------------
% 5.96/2.14  % (8094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.14  % (8094)Termination reason: Unknown
% 5.96/2.14  % (8094)Termination phase: Preprocessing 3
% 5.96/2.14  
% 5.96/2.14  % (8094)Memory used [KB]: 2046
% 5.96/2.14  % (8094)Time elapsed: 0.024 s
% 5.96/2.14  % (8094)Instructions burned: 47 (million)
% 5.96/2.14  % (8094)------------------------------
% 5.96/2.14  % (8094)------------------------------
% 5.96/2.15  % (8102)Instruction limit reached!
% 5.96/2.15  % (8102)------------------------------
% 5.96/2.15  % (8102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.15  % (8102)Termination reason: Unknown
% 5.96/2.15  % (8102)Termination phase: Property scanning
% 5.96/2.15  
% 5.96/2.15  % (8102)Memory used [KB]: 1791
% 5.96/2.15  % (8102)Time elapsed: 0.011 s
% 5.96/2.15  % (8102)Instructions burned: 32 (million)
% 5.96/2.15  % (8102)------------------------------
% 5.96/2.15  % (8102)------------------------------
% 5.96/2.15  % (8103)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7835 for (2995ds/96Mi)
% 5.96/2.16  % (8104)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_7835 for (2995ds/453Mi)
% 5.96/2.16  % (8101)Instruction limit reached!
% 5.96/2.16  % (8101)------------------------------
% 5.96/2.16  % (8101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.16  % (8101)Termination reason: Unknown
% 5.96/2.16  % (8101)Termination phase: Property scanning
% 5.96/2.16  
% 5.96/2.16  % (8101)Memory used [KB]: 2174
% 5.96/2.16  % (8101)Time elapsed: 0.030 s
% 5.96/2.16  % (8101)Instructions burned: 63 (million)
% 5.96/2.16  % (8101)------------------------------
% 5.96/2.16  % (8101)------------------------------
% 5.96/2.18  % (8032)Instruction limit reached!
% 5.96/2.18  % (8032)------------------------------
% 5.96/2.18  % (8032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.18  % (8032)Termination reason: Unknown
% 5.96/2.18  % (8032)Termination phase: Saturation
% 5.96/2.18  
% 5.96/2.18  % (8032)Memory used [KB]: 9722
% 5.96/2.18  % (8032)Time elapsed: 0.477 s
% 5.96/2.18  % (8032)Instructions burned: 1042 (million)
% 5.96/2.18  % (8032)------------------------------
% 5.96/2.18  % (8032)------------------------------
% 5.96/2.18  % (8106)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_7835 for (2994ds/71Mi)
% 5.96/2.19  % (8074)Instruction limit reached!
% 5.96/2.19  % (8074)------------------------------
% 5.96/2.19  % (8074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.19  % (8074)Termination reason: Unknown
% 5.96/2.19  % (8074)Termination phase: Saturation
% 5.96/2.19  
% 5.96/2.19  % (8074)Memory used [KB]: 7675
% 5.96/2.19  % (8074)Time elapsed: 0.235 s
% 5.96/2.19  % (8074)Instructions burned: 449 (million)
% 5.96/2.19  % (8074)------------------------------
% 5.96/2.19  % (8074)------------------------------
% 5.96/2.19  % (8109)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7835 for (2994ds/83Mi)
% 5.96/2.19  % (8103)Instruction limit reached!
% 5.96/2.19  % (8103)------------------------------
% 5.96/2.19  % (8103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.19  % (8103)Termination reason: Unknown
% 5.96/2.19  % (8103)Termination phase: Property scanning
% 5.96/2.19  
% 5.96/2.19  % (8103)Memory used [KB]: 2174
% 5.96/2.19  % (8103)Time elapsed: 0.041 s
% 5.96/2.19  % (8103)Instructions burned: 96 (million)
% 5.96/2.19  % (8103)------------------------------
% 5.96/2.19  % (8103)------------------------------
% 6.28/2.20  % (8110)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7835 for (2994ds/11Mi)
% 6.28/2.21  % (8110)Instruction limit reached!
% 6.28/2.21  % (8110)------------------------------
% 6.28/2.21  % (8110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.21  % (8110)Termination reason: Unknown
% 6.28/2.21  % (8110)Termination phase: shuffling
% 6.28/2.21  
% 6.28/2.21  % (8110)Memory used [KB]: 1535
% 6.28/2.21  % (8110)Time elapsed: 0.007 s
% 6.28/2.21  % (8110)Instructions burned: 12 (million)
% 6.28/2.21  % (8110)------------------------------
% 6.28/2.21  % (8110)------------------------------
% 6.28/2.21  % (8112)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_7835 for (2994ds/41Mi)
% 6.28/2.21  % (8106)Instruction limit reached!
% 6.28/2.21  % (8106)------------------------------
% 6.28/2.21  % (8106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.21  % (8106)Termination reason: Unknown
% 6.28/2.21  % (8106)Termination phase: Property scanning
% 6.28/2.21  
% 6.28/2.21  % (8106)Memory used [KB]: 2174
% 6.28/2.21  % (8106)Time elapsed: 0.036 s
% 6.28/2.21  % (8106)Instructions burned: 72 (million)
% 6.28/2.21  % (8106)------------------------------
% 6.28/2.21  % (8106)------------------------------
% 6.28/2.22  % (8109)Instruction limit reached!
% 6.28/2.22  % (8109)------------------------------
% 6.28/2.22  % (8109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.22  % (8109)Termination reason: Unknown
% 6.28/2.22  % (8109)Termination phase: Saturation
% 6.28/2.22  
% 6.28/2.22  % (8109)Memory used [KB]: 6524
% 6.28/2.22  % (8109)Time elapsed: 0.035 s
% 6.28/2.22  % (8109)Instructions burned: 83 (million)
% 6.28/2.22  % (8109)------------------------------
% 6.28/2.22  % (8109)------------------------------
% 6.28/2.22  % (8113)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7835 for (2994ds/6Mi)
% 6.28/2.23  % (8113)Instruction limit reached!
% 6.28/2.23  % (8113)------------------------------
% 6.28/2.23  % (8113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.23  % (8113)Termination reason: Unknown
% 6.28/2.23  % (8113)Termination phase: shuffling
% 6.28/2.23  
% 6.28/2.23  % (8113)Memory used [KB]: 1407
% 6.28/2.23  % (8113)Time elapsed: 0.005 s
% 6.28/2.23  % (8113)Instructions burned: 7 (million)
% 6.28/2.23  % (8113)------------------------------
% 6.28/2.23  % (8113)------------------------------
% 6.28/2.23  % (8112)Instruction limit reached!
% 6.28/2.23  % (8112)------------------------------
% 6.28/2.23  % (8112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.23  % (8112)Termination reason: Unknown
% 6.28/2.23  % (8112)Termination phase: shuffling
% 6.28/2.23  
% 6.28/2.23  % (8112)Memory used [KB]: 2174
% 6.28/2.23  % (8112)Time elapsed: 0.017 s
% 6.28/2.23  % (8112)Instructions burned: 42 (million)
% 6.28/2.23  % (8112)------------------------------
% 6.28/2.23  % (8112)------------------------------
% 6.28/2.24  % (8115)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7835 for (2994ds/150Mi)
% 6.28/2.24  % (8117)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7835 for (2994ds/343Mi)
% 6.28/2.24  % (8118)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_7835 for (2994ds/109Mi)
% 6.28/2.24  % (8119)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_7835 for (2994ds/253Mi)
% 6.28/2.29  % (8118)Instruction limit reached!
% 6.28/2.29  % (8118)------------------------------
% 6.28/2.29  % (8118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.29  % (8118)Termination reason: Unknown
% 6.28/2.29  % (8118)Termination phase: Property scanning
% 6.28/2.29  
% 6.28/2.29  % (8118)Memory used [KB]: 2174
% 6.28/2.29  % (8118)Time elapsed: 0.052 s
% 6.28/2.29  % (8118)Instructions burned: 110 (million)
% 6.28/2.29  % (8118)------------------------------
% 6.28/2.29  % (8118)------------------------------
% 6.51/2.31  % (8115)Instruction limit reached!
% 6.51/2.31  % (8115)------------------------------
% 6.51/2.31  % (8115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.31  % (8115)Termination reason: Unknown
% 6.51/2.31  % (8115)Termination phase: Saturation
% 6.51/2.31  
% 6.51/2.31  % (8115)Memory used [KB]: 6908
% 6.51/2.31  % (8115)Time elapsed: 0.071 s
% 6.51/2.31  % (8115)Instructions burned: 151 (million)
% 6.51/2.31  % (8115)------------------------------
% 6.51/2.31  % (8115)------------------------------
% 6.51/2.32  % (8123)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7835 for (2993ds/140Mi)
% 6.51/2.32  % (8124)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_7835 for (2993ds/614Mi)
% 6.51/2.33  % (8100)Instruction limit reached!
% 6.51/2.33  % (8100)------------------------------
% 6.51/2.33  % (8100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.33  % (8100)Termination reason: Unknown
% 6.51/2.33  % (8100)Termination phase: Saturation
% 6.51/2.33  
% 6.51/2.33  % (8100)Memory used [KB]: 3582
% 6.51/2.33  % (8100)Time elapsed: 0.208 s
% 6.51/2.33  % (8100)Instructions burned: 433 (million)
% 6.51/2.33  % (8100)------------------------------
% 6.51/2.33  % (8100)------------------------------
% 6.51/2.35  % (8125)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_7835 for (2993ds/202Mi)
% 6.51/2.36  % (8104)Instruction limit reached!
% 6.51/2.36  % (8104)------------------------------
% 6.51/2.36  % (8104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.36  % (8104)Termination reason: Unknown
% 6.51/2.36  % (8104)Termination phase: Saturation
% 6.51/2.36  
% 6.51/2.36  % (8104)Memory used [KB]: 7803
% 6.51/2.36  % (8104)Time elapsed: 0.206 s
% 6.51/2.36  % (8104)Instructions burned: 453 (million)
% 6.51/2.36  % (8104)------------------------------
% 6.51/2.36  % (8104)------------------------------
% 6.51/2.36  % (8119)Instruction limit reached!
% 6.51/2.36  % (8119)------------------------------
% 6.51/2.36  % (8119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.36  % (8119)Termination reason: Unknown
% 6.51/2.36  % (8119)Termination phase: Saturation
% 6.51/2.36  
% 6.51/2.36  % (8119)Memory used [KB]: 6780
% 6.51/2.36  % (8119)Time elapsed: 0.120 s
% 6.51/2.36  % (8119)Instructions burned: 255 (million)
% 6.51/2.36  % (8119)------------------------------
% 6.51/2.36  % (8119)------------------------------
% 6.51/2.37  % (8129)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_7835 for (2992ds/339Mi)
% 6.51/2.38  % (8130)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_7835 for (2992ds/283Mi)
% 6.51/2.38  % (8125)Refutation not found, incomplete strategy
% 6.51/2.38  % (8125)------------------------------
% 6.51/2.38  % (8125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.38  % (8125)Termination reason: Refutation not found, incomplete strategy
% 6.51/2.38  
% 6.51/2.38  
% 6.51/2.38  % (8125)Memory used [KB]: 6652
% 6.51/2.38  % (8125)Time elapsed: 0.036 s
% 6.51/2.38  % (8125)Instructions burned: 70 (million)
% 6.51/2.38  % (8125)------------------------------
% 6.51/2.38  % (8125)------------------------------
% 6.51/2.39  % (8117)Instruction limit reached!
% 6.51/2.39  % (8117)------------------------------
% 6.51/2.39  % (8117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.39  % (8117)Termination reason: Unknown
% 6.51/2.39  % (8117)Termination phase: Saturation
% 6.51/2.39  
% 6.51/2.39  % (8117)Memory used [KB]: 7419
% 6.51/2.39  % (8117)Time elapsed: 0.149 s
% 6.51/2.39  % (8117)Instructions burned: 343 (million)
% 6.51/2.39  % (8117)------------------------------
% 6.51/2.39  % (8117)------------------------------
% 6.51/2.39  % (8123)Instruction limit reached!
% 6.51/2.39  % (8123)------------------------------
% 6.51/2.39  % (8123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.39  % (8123)Termination reason: Unknown
% 6.51/2.39  % (8123)Termination phase: Saturation
% 6.51/2.39  
% 6.51/2.39  % (8123)Memory used [KB]: 6780
% 6.51/2.39  % (8123)Time elapsed: 0.098 s
% 6.51/2.39  % (8123)Instructions burned: 140 (million)
% 6.51/2.39  % (8123)------------------------------
% 6.51/2.39  % (8123)------------------------------
% 7.46/2.40  % (8133)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7835 for (2992ds/298Mi)
% 7.46/2.41  % (8132)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7835 for (2992ds/134Mi)
% 7.46/2.41  % (8134)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7835 for (2992ds/192Mi)
% 7.46/2.47  % (8132)Instruction limit reached!
% 7.46/2.47  % (8132)------------------------------
% 7.46/2.47  % (8132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.47  % (8132)Termination reason: Unknown
% 7.46/2.47  % (8132)Termination phase: Saturation
% 7.46/2.47  
% 7.46/2.47  % (8132)Memory used [KB]: 6780
% 7.46/2.47  % (8132)Time elapsed: 0.063 s
% 7.46/2.47  % (8132)Instructions burned: 134 (million)
% 7.46/2.47  % (8132)------------------------------
% 7.46/2.47  % (8132)------------------------------
% 7.46/2.48  % (8129)Instruction limit reached!
% 7.46/2.48  % (8129)------------------------------
% 7.46/2.48  % (8129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.48  % (8129)Termination reason: Unknown
% 7.46/2.48  % (8129)Termination phase: Saturation
% 7.46/2.48  
% 7.46/2.48  % (8129)Memory used [KB]: 6780
% 7.46/2.48  % (8129)Time elapsed: 0.108 s
% 7.46/2.48  % (8129)Instructions burned: 340 (million)
% 7.46/2.48  % (8129)------------------------------
% 7.46/2.48  % (8129)------------------------------
% 7.46/2.49  % (8134)Instruction limit reached!
% 7.46/2.49  % (8134)------------------------------
% 7.46/2.49  % (8134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.49  % (8134)Termination reason: Unknown
% 7.46/2.49  % (8134)Termination phase: Saturation
% 7.46/2.49  
% 7.46/2.49  % (8134)Memory used [KB]: 3070
% 7.46/2.49  % (8134)Time elapsed: 0.080 s
% 7.46/2.49  % (8134)Instructions burned: 193 (million)
% 7.46/2.49  % (8134)------------------------------
% 7.46/2.49  % (8134)------------------------------
% 7.46/2.49  % (8141)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_7835 for (2991ds/258Mi)
% 7.46/2.49  % (8142)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_7835 for (2991ds/90Mi)
% 7.75/2.51  % (8143)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_7835 for (2991ds/231Mi)
% 7.75/2.51  % (8130)Instruction limit reached!
% 7.75/2.51  % (8130)------------------------------
% 7.75/2.51  % (8130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.51  % (8130)Termination reason: Unknown
% 7.75/2.51  % (8130)Termination phase: Saturation
% 7.75/2.51  
% 7.75/2.51  % (8130)Memory used [KB]: 7547
% 7.75/2.51  % (8130)Time elapsed: 0.134 s
% 7.75/2.51  % (8130)Instructions burned: 284 (million)
% 7.75/2.51  % (8130)------------------------------
% 7.75/2.51  % (8130)------------------------------
% 7.75/2.53  % (8146)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_7835 for (2991ds/458Mi)
% 7.75/2.53  % (8133)Instruction limit reached!
% 7.75/2.53  % (8133)------------------------------
% 7.75/2.53  % (8133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.53  % (8133)Termination reason: Unknown
% 7.75/2.53  % (8133)Termination phase: Saturation
% 7.75/2.53  
% 7.75/2.53  % (8133)Memory used [KB]: 7291
% 7.75/2.53  % (8133)Time elapsed: 0.132 s
% 7.75/2.53  % (8133)Instructions burned: 298 (million)
% 7.75/2.53  % (8133)------------------------------
% 7.75/2.53  % (8133)------------------------------
% 7.75/2.54  % (8142)Instruction limit reached!
% 7.75/2.54  % (8142)------------------------------
% 7.75/2.54  % (8142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.54  % (8142)Termination reason: Unknown
% 7.75/2.54  % (8142)Termination phase: Property scanning
% 7.75/2.54  
% 7.75/2.54  % (8142)Memory used [KB]: 2174
% 7.75/2.54  % (8142)Time elapsed: 0.043 s
% 7.75/2.54  % (8142)Instructions burned: 92 (million)
% 7.75/2.54  % (8142)------------------------------
% 7.75/2.54  % (8142)------------------------------
% 7.75/2.54  % (8150)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_7835 for (2991ds/297Mi)
% 7.75/2.55  % (8149)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_7835 for (2991ds/31Mi)
% 7.75/2.56  % (8092)Instruction limit reached!
% 7.75/2.56  % (8092)------------------------------
% 7.75/2.56  % (8092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.56  % (8092)Termination reason: Unknown
% 7.75/2.56  % (8092)Termination phase: Saturation
% 7.75/2.56  
% 7.75/2.56  % (8092)Memory used [KB]: 7803
% 7.75/2.56  % (8092)Time elapsed: 0.451 s
% 7.75/2.56  % (8092)Instructions burned: 1087 (million)
% 7.75/2.56  % (8092)------------------------------
% 7.75/2.56  % (8092)------------------------------
% 7.75/2.57  % (8149)Instruction limit reached!
% 7.75/2.57  % (8149)------------------------------
% 7.75/2.57  % (8149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.57  % (8149)Termination reason: Unknown
% 7.75/2.57  % (8149)Termination phase: Property scanning
% 7.75/2.57  
% 7.75/2.57  % (8149)Memory used [KB]: 1791
% 7.75/2.57  % (8149)Time elapsed: 0.018 s
% 7.75/2.57  % (8149)Instructions burned: 33 (million)
% 7.75/2.57  % (8149)------------------------------
% 7.75/2.57  % (8149)------------------------------
% 7.75/2.58  % (8153)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_7835 for (2990ds/987Mi)
% 7.75/2.58  % (8154)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_7835 for (2990ds/182Mi)
% 8.59/2.60  % (8143)Instruction limit reached!
% 8.59/2.60  % (8143)------------------------------
% 8.59/2.60  % (8143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.60  % (8143)Termination reason: Unknown
% 8.59/2.60  % (8143)Termination phase: Saturation
% 8.59/2.60  
% 8.59/2.60  % (8143)Memory used [KB]: 7036
% 8.59/2.60  % (8143)Time elapsed: 0.087 s
% 8.59/2.60  % (8143)Instructions burned: 232 (million)
% 8.59/2.60  % (8143)------------------------------
% 8.59/2.60  % (8143)------------------------------
% 8.59/2.60  % (8124)Instruction limit reached!
% 8.59/2.60  % (8124)------------------------------
% 8.59/2.60  % (8124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.60  % (8124)Termination reason: Unknown
% 8.59/2.60  % (8124)Termination phase: Saturation
% 8.59/2.60  
% 8.59/2.60  % (8124)Memory used [KB]: 8187
% 8.59/2.60  % (8124)Time elapsed: 0.279 s
% 8.59/2.60  % (8124)Instructions burned: 617 (million)
% 8.59/2.60  % (8124)------------------------------
% 8.59/2.60  % (8124)------------------------------
% 8.59/2.61  % (8158)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_7835 for (2990ds/154Mi)
% 8.59/2.61  % (8157)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_7835 for (2990ds/182Mi)
% 8.59/2.62  % (8141)Instruction limit reached!
% 8.59/2.62  % (8141)------------------------------
% 8.59/2.62  % (8141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.62  % (8141)Termination reason: Unknown
% 8.59/2.62  % (8141)Termination phase: Saturation
% 8.59/2.62  
% 8.59/2.62  % (8141)Memory used [KB]: 7291
% 8.59/2.62  % (8141)Time elapsed: 0.144 s
% 8.59/2.62  % (8141)Instructions burned: 260 (million)
% 8.59/2.62  % (8141)------------------------------
% 8.59/2.62  % (8141)------------------------------
% 8.59/2.63  % (8160)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_7835 for (2990ds/79Mi)
% 8.59/2.66  % (8160)Instruction limit reached!
% 8.59/2.66  % (8160)------------------------------
% 8.59/2.66  % (8160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.66  % (8160)Termination reason: Unknown
% 8.59/2.66  % (8160)Termination phase: Property scanning
% 8.59/2.66  
% 8.59/2.66  % (8160)Memory used [KB]: 2174
% 8.59/2.66  % (8160)Time elapsed: 0.028 s
% 8.59/2.66  % (8160)Instructions burned: 80 (million)
% 8.59/2.66  % (8160)------------------------------
% 8.59/2.66  % (8160)------------------------------
% 8.59/2.66  % (8154)Instruction limit reached!
% 8.59/2.66  % (8154)------------------------------
% 8.59/2.66  % (8154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.66  % (8154)Termination reason: Unknown
% 8.59/2.66  % (8154)Termination phase: Saturation
% 8.59/2.66  
% 8.59/2.66  % (8154)Memory used [KB]: 6908
% 8.59/2.66  % (8154)Time elapsed: 0.081 s
% 8.59/2.66  % (8154)Instructions burned: 183 (million)
% 8.59/2.66  % (8154)------------------------------
% 8.59/2.66  % (8154)------------------------------
% 8.59/2.66  % (8150)Instruction limit reached!
% 8.59/2.66  % (8150)------------------------------
% 8.59/2.66  % (8150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.66  % (8150)Termination reason: Unknown
% 8.59/2.66  % (8150)Termination phase: Saturation
% 8.59/2.66  
% 8.59/2.66  % (8150)Memory used [KB]: 7036
% 8.59/2.66  % (8150)Time elapsed: 0.120 s
% 8.59/2.66  % (8150)Instructions burned: 297 (million)
% 8.59/2.66  % (8150)------------------------------
% 8.59/2.66  % (8150)------------------------------
% 8.59/2.67  % (8163)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_7835 for (2990ds/216Mi)
% 8.59/2.67  % (8158)Instruction limit reached!
% 8.59/2.67  % (8158)------------------------------
% 8.59/2.67  % (8158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.67  % (8158)Termination reason: Unknown
% 8.59/2.67  % (8158)Termination phase: Saturation
% 8.59/2.67  
% 8.59/2.67  % (8158)Memory used [KB]: 2430
% 8.59/2.67  % (8158)Time elapsed: 0.067 s
% 8.59/2.67  % (8158)Instructions burned: 154 (million)
% 8.59/2.67  % (8158)------------------------------
% 8.59/2.67  % (8158)------------------------------
% 8.59/2.68  % (8165)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_7835 for (2989ds/922Mi)
% 8.59/2.68  % (8164)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7835 for (2990ds/114Mi)
% 8.59/2.69  % (8167)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_7835 for (2989ds/182Mi)
% 9.44/2.70  % (8157)Instruction limit reached!
% 9.44/2.70  % (8157)------------------------------
% 9.44/2.70  % (8157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.70  % (8157)Termination reason: Unknown
% 9.44/2.70  % (8157)Termination phase: Saturation
% 9.44/2.70  
% 9.44/2.70  % (8157)Memory used [KB]: 7036
% 9.44/2.70  % (8157)Time elapsed: 0.112 s
% 9.44/2.70  % (8157)Instructions burned: 182 (million)
% 9.44/2.70  % (8157)------------------------------
% 9.44/2.70  % (8157)------------------------------
% 9.44/2.72  % (8146)Instruction limit reached!
% 9.44/2.72  % (8146)------------------------------
% 9.44/2.72  % (8146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.72  % (8146)Termination reason: Unknown
% 9.44/2.72  % (8146)Termination phase: Saturation
% 9.44/2.72  
% 9.44/2.72  % (8146)Memory used [KB]: 8187
% 9.44/2.72  % (8146)Time elapsed: 0.175 s
% 9.44/2.72  % (8146)Instructions burned: 458 (million)
% 9.44/2.72  % (8146)------------------------------
% 9.44/2.72  % (8146)------------------------------
% 9.44/2.72  % (8168)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_7835 for (2989ds/164Mi)
% 9.44/2.73  % (8170)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_7835 for (2989ds/50Mi)
% 9.44/2.74  % (8164)Instruction limit reached!
% 9.44/2.74  % (8164)------------------------------
% 9.44/2.74  % (8164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.74  % (8164)Termination reason: Unknown
% 9.44/2.74  % (8164)Termination phase: Saturation
% 9.44/2.74  
% 9.44/2.74  % (8164)Memory used [KB]: 6652
% 9.44/2.74  % (8164)Time elapsed: 0.034 s
% 9.44/2.74  % (8164)Instructions burned: 115 (million)
% 9.44/2.74  % (8164)------------------------------
% 9.44/2.74  % (8164)------------------------------
% 9.44/2.75  % (8172)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7835 for (2989ds/368Mi)
% 9.44/2.76  % (8170)Instruction limit reached!
% 9.44/2.76  % (8170)------------------------------
% 9.44/2.76  % (8170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.76  % (8170)Termination reason: Unknown
% 9.44/2.76  % (8170)Termination phase: Property scanning
% 9.44/2.76  
% 9.44/2.76  % (8170)Memory used [KB]: 2174
% 9.44/2.76  % (8170)Time elapsed: 0.025 s
% 9.44/2.76  % (8170)Instructions burned: 51 (million)
% 9.44/2.76  % (8170)------------------------------
% 9.44/2.76  % (8170)------------------------------
% 9.44/2.76  % (8167)Instruction limit reached!
% 9.44/2.76  % (8167)------------------------------
% 9.44/2.76  % (8167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.76  % (8167)Termination reason: Unknown
% 9.44/2.76  % (8167)Termination phase: Saturation
% 9.44/2.76  
% 9.44/2.76  % (8167)Memory used [KB]: 6908
% 9.44/2.76  % (8167)Time elapsed: 0.074 s
% 9.44/2.76  % (8167)Instructions burned: 182 (million)
% 9.44/2.76  % (8167)------------------------------
% 9.44/2.76  % (8167)------------------------------
% 9.44/2.77  % (8163)Instruction limit reached!
% 9.44/2.77  % (8163)------------------------------
% 9.44/2.77  % (8163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.77  % (8163)Termination reason: Unknown
% 9.44/2.77  % (8163)Termination phase: Saturation
% 9.44/2.77  
% 9.44/2.77  % (8163)Memory used [KB]: 7164
% 9.44/2.77  % (8163)Time elapsed: 0.096 s
% 9.44/2.77  % (8163)Instructions burned: 217 (million)
% 9.44/2.77  % (8163)------------------------------
% 9.44/2.77  % (8163)------------------------------
% 9.44/2.77  % (8175)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_7835 for (2988ds/1021Mi)
% 9.44/2.78  % (8168)Instruction limit reached!
% 9.44/2.78  % (8168)------------------------------
% 9.44/2.78  % (8168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.78  % (8168)Termination reason: Unknown
% 9.44/2.78  % (8168)Termination phase: Saturation
% 9.44/2.78  
% 9.44/2.78  % (8168)Memory used [KB]: 2430
% 9.44/2.78  % (8168)Time elapsed: 0.061 s
% 9.44/2.78  % (8168)Instructions burned: 165 (million)
% 9.44/2.78  % (8168)------------------------------
% 9.44/2.78  % (8168)------------------------------
% 9.44/2.79  % (8176)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_7835 for (2988ds/267Mi)
% 9.44/2.79  % (8178)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_7835 for (2988ds/26Mi)
% 10.09/2.80  % (8177)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_7835 for (2988ds/204Mi)
% 10.09/2.81  % (8178)Instruction limit reached!
% 10.09/2.81  % (8178)------------------------------
% 10.09/2.81  % (8178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.81  % (8178)Termination reason: Unknown
% 10.09/2.81  % (8178)Termination phase: shuffling
% 10.09/2.81  
% 10.09/2.81  % (8178)Memory used [KB]: 1791
% 10.09/2.81  % (8178)Time elapsed: 0.014 s
% 10.09/2.81  % (8178)Instructions burned: 27 (million)
% 10.09/2.81  % (8178)------------------------------
% 10.09/2.81  % (8178)------------------------------
% 10.09/2.82  % (8179)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_7835 for (2988ds/53Mi)
% 10.09/2.85  % (8179)Instruction limit reached!
% 10.09/2.85  % (8179)------------------------------
% 10.09/2.85  % (8179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.85  % (8179)Termination reason: Unknown
% 10.09/2.85  % (8179)Termination phase: Property scanning
% 10.09/2.85  
% 10.09/2.85  % (8179)Memory used [KB]: 2174
% 10.09/2.85  % (8179)Time elapsed: 0.026 s
% 10.09/2.85  % (8179)Instructions burned: 54 (million)
% 10.09/2.85  % (8179)------------------------------
% 10.09/2.85  % (8179)------------------------------
% 10.09/2.86  % (8176)Instruction limit reached!
% 10.09/2.86  % (8176)------------------------------
% 10.09/2.86  % (8176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.86  % (8176)Termination reason: Unknown
% 10.09/2.86  % (8176)Termination phase: Saturation
% 10.09/2.86  
% 10.09/2.86  % (8176)Memory used [KB]: 7419
% 10.09/2.86  % (8176)Time elapsed: 0.077 s
% 10.09/2.86  % (8176)Instructions burned: 267 (million)
% 10.09/2.86  % (8176)------------------------------
% 10.09/2.86  % (8176)------------------------------
% 10.09/2.87  % (8180)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_7835 for (2988ds/4436Mi)
% 10.09/2.88  % (8182)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_7835 for (2987ds/1539Mi)
% 10.24/2.91  % (8172)Instruction limit reached!
% 10.24/2.91  % (8172)------------------------------
% 10.24/2.91  % (8172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.91  % (8172)Termination reason: Unknown
% 10.24/2.91  % (8172)Termination phase: Saturation
% 10.24/2.91  
% 10.24/2.91  % (8172)Memory used [KB]: 7675
% 10.24/2.91  % (8172)Time elapsed: 0.167 s
% 10.24/2.91  % (8172)Instructions burned: 369 (million)
% 10.24/2.91  % (8172)------------------------------
% 10.24/2.91  % (8172)------------------------------
% 10.24/2.91  % (8177)Instruction limit reached!
% 10.24/2.91  % (8177)------------------------------
% 10.24/2.91  % (8177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.91  % (8177)Termination reason: Unknown
% 10.24/2.91  % (8177)Termination phase: Saturation
% 10.24/2.91  
% 10.24/2.91  % (8177)Memory used [KB]: 7164
% 10.24/2.91  % (8177)Time elapsed: 0.063 s
% 10.24/2.91  % (8177)Instructions burned: 205 (million)
% 10.24/2.91  % (8177)------------------------------
% 10.24/2.91  % (8177)------------------------------
% 10.24/2.93  % (8183)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_7835 for (2987ds/408Mi)
% 10.24/2.93  % (8184)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_7835 for (2987ds/5205Mi)
% 11.99/3.03  % (8153)Instruction limit reached!
% 11.99/3.03  % (8153)------------------------------
% 11.99/3.03  % (8153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.99/3.03  % (8153)Termination reason: Unknown
% 11.99/3.03  % (8153)Termination phase: Saturation
% 11.99/3.03  
% 11.99/3.03  % (8153)Memory used [KB]: 9594
% 11.99/3.03  % (8153)Time elapsed: 0.474 s
% 11.99/3.03  % (8153)Instructions burned: 989 (million)
% 11.99/3.03  % (8153)------------------------------
% 11.99/3.03  % (8153)------------------------------
% 11.99/3.05  % (8188)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_7835 for (2986ds/1913Mi)
% 11.99/3.11  % (8183)Instruction limit reached!
% 11.99/3.11  % (8183)------------------------------
% 11.99/3.11  % (8183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.99/3.11  % (8183)Termination reason: Unknown
% 11.99/3.11  % (8183)Termination phase: Saturation
% 11.99/3.11  
% 11.99/3.11  % (8183)Memory used [KB]: 8059
% 11.99/3.11  % (8183)Time elapsed: 0.179 s
% 11.99/3.11  % (8183)Instructions burned: 408 (million)
% 11.99/3.11  % (8183)------------------------------
% 11.99/3.11  % (8183)------------------------------
% 11.99/3.12  % (8191)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_7835 for (2985ds/4350Mi)
% 12.61/3.13  % (8165)Instruction limit reached!
% 12.61/3.13  % (8165)------------------------------
% 12.61/3.13  % (8165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.61/3.13  % (8165)Termination reason: Unknown
% 12.61/3.13  % (8165)Termination phase: Saturation
% 12.61/3.13  
% 12.61/3.13  % (8165)Memory used [KB]: 7547
% 12.61/3.13  % (8165)Time elapsed: 0.450 s
% 12.61/3.13  % (8165)Instructions burned: 922 (million)
% 12.61/3.13  % (8165)------------------------------
% 12.61/3.13  % (8165)------------------------------
% 12.61/3.14  % (8193)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_7835 for (2985ds/68Mi)
% 12.61/3.18  % (8193)Instruction limit reached!
% 12.61/3.18  % (8193)------------------------------
% 12.61/3.18  % (8193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.61/3.18  % (8193)Termination reason: Unknown
% 12.61/3.18  % (8193)Termination phase: Property scanning
% 12.61/3.18  
% 12.61/3.18  % (8193)Memory used [KB]: 2174
% 12.61/3.18  % (8193)Time elapsed: 0.035 s
% 12.61/3.18  % (8193)Instructions burned: 69 (million)
% 12.61/3.18  % (8193)------------------------------
% 12.61/3.18  % (8193)------------------------------
% 12.96/3.20  % (8175)Instruction limit reached!
% 12.96/3.20  % (8175)------------------------------
% 12.96/3.20  % (8175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.20  % (8175)Termination reason: Unknown
% 12.96/3.20  % (8175)Termination phase: Saturation
% 12.96/3.20  
% 12.96/3.20  % (8175)Memory used [KB]: 9466
% 12.96/3.20  % (8175)Time elapsed: 0.431 s
% 12.96/3.20  % (8175)Instructions burned: 1021 (million)
% 12.96/3.20  % (8175)------------------------------
% 12.96/3.20  % (8175)------------------------------
% 12.96/3.20  % (8194)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_7835 for (2984ds/358Mi)
% 12.96/3.21  % (8195)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_7835 for (2984ds/31Mi)
% 12.96/3.23  % (8195)Instruction limit reached!
% 12.96/3.23  % (8195)------------------------------
% 12.96/3.23  % (8195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.23  % (8195)Termination reason: Unknown
% 12.96/3.23  % (8195)Termination phase: Property scanning
% 12.96/3.23  
% 12.96/3.23  % (8195)Memory used [KB]: 1791
% 12.96/3.23  % (8195)Time elapsed: 0.017 s
% 12.96/3.23  % (8195)Instructions burned: 32 (million)
% 12.96/3.23  % (8195)------------------------------
% 12.96/3.23  % (8195)------------------------------
% 12.96/3.24  % (8197)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7835 for (2984ds/279Mi)
% 12.96/3.29  % (8197)Refutation not found, incomplete strategy
% 12.96/3.29  % (8197)------------------------------
% 12.96/3.29  % (8197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.29  % (8197)Termination reason: Refutation not found, incomplete strategy
% 12.96/3.29  
% 12.96/3.29  
% 12.96/3.29  % (8197)Memory used [KB]: 6908
% 12.96/3.29  % (8197)Time elapsed: 0.045 s
% 12.96/3.29  % (8197)Instructions burned: 113 (million)
% 12.96/3.29  % (8197)------------------------------
% 12.96/3.29  % (8197)------------------------------
% 13.35/3.30  % (8200)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7835 for (2983ds/258Mi)
% 13.35/3.36  % (8194)Instruction limit reached!
% 13.35/3.36  % (8194)------------------------------
% 13.35/3.36  % (8194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.36  % (8194)Termination reason: Unknown
% 13.35/3.36  % (8194)Termination phase: Saturation
% 13.35/3.36  
% 13.35/3.36  % (8194)Memory used [KB]: 7547
% 13.35/3.36  % (8194)Time elapsed: 0.159 s
% 13.35/3.36  % (8194)Instructions burned: 359 (million)
% 13.35/3.36  % (8194)------------------------------
% 13.35/3.36  % (8194)------------------------------
% 13.35/3.38  % (8202)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_7835 for (2982ds/26Mi)
% 13.35/3.39  % (8202)Instruction limit reached!
% 13.35/3.39  % (8202)------------------------------
% 13.35/3.39  % (8202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.39  % (8202)Termination reason: Unknown
% 13.35/3.39  % (8202)Termination phase: shuffling
% 13.35/3.39  
% 13.35/3.39  % (8202)Memory used [KB]: 1791
% 13.35/3.39  % (8202)Time elapsed: 0.014 s
% 13.35/3.39  % (8202)Instructions burned: 27 (million)
% 13.35/3.39  % (8202)------------------------------
% 13.35/3.39  % (8202)------------------------------
% 13.85/3.40  % (8203)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_7835 for (2982ds/995Mi)
% 13.85/3.43  % (8200)Instruction limit reached!
% 13.85/3.43  % (8200)------------------------------
% 13.85/3.43  % (8200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.43  % (8200)Termination reason: Unknown
% 13.85/3.43  % (8200)Termination phase: Saturation
% 13.85/3.43  
% 13.85/3.43  % (8200)Memory used [KB]: 7291
% 13.85/3.43  % (8200)Time elapsed: 0.126 s
% 13.85/3.43  % (8200)Instructions burned: 259 (million)
% 13.85/3.43  % (8200)------------------------------
% 13.85/3.43  % (8200)------------------------------
% 13.85/3.45  % (8205)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_7835 for (2982ds/373Mi)
% 14.60/3.60  % (8182)Instruction limit reached!
% 14.60/3.60  % (8182)------------------------------
% 14.60/3.60  % (8182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.60/3.60  % (8182)Termination reason: Unknown
% 14.60/3.60  % (8182)Termination phase: Saturation
% 14.60/3.60  
% 14.60/3.60  % (8182)Memory used [KB]: 11001
% 14.60/3.60  % (8182)Time elapsed: 0.727 s
% 14.60/3.60  % (8182)Instructions burned: 1540 (million)
% 14.60/3.60  % (8182)------------------------------
% 14.60/3.60  % (8182)------------------------------
% 14.60/3.61  % (8205)Instruction limit reached!
% 14.60/3.61  % (8205)------------------------------
% 14.60/3.61  % (8205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.60/3.61  % (8205)Termination reason: Unknown
% 14.60/3.61  % (8205)Termination phase: Saturation
% 14.60/3.61  
% 14.60/3.61  % (8205)Memory used [KB]: 8059
% 14.60/3.61  % (8205)Time elapsed: 0.164 s
% 14.60/3.61  % (8205)Instructions burned: 374 (million)
% 14.60/3.61  % (8205)------------------------------
% 14.60/3.61  % (8205)------------------------------
% 14.60/3.62  % (8212)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_7835 for (2980ds/253Mi)
% 14.60/3.62  % (8213)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_7835 for (2980ds/832Mi)
% 14.60/3.68  % (8212)Instruction limit reached!
% 14.60/3.68  % (8212)------------------------------
% 14.60/3.68  % (8212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.60/3.68  % (8212)Termination reason: Unknown
% 14.60/3.68  % (8212)Termination phase: Saturation
% 14.60/3.68  
% 14.60/3.68  % (8212)Memory used [KB]: 7419
% 14.60/3.68  % (8212)Time elapsed: 0.070 s
% 14.60/3.68  % (8212)Instructions burned: 254 (million)
% 14.60/3.68  % (8212)------------------------------
% 14.60/3.68  % (8212)------------------------------
% 14.60/3.69  % (8216)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_7835 for (2979ds/668Mi)
% 14.60/3.69  % (8213)Refutation not found, incomplete strategy
% 14.60/3.69  % (8213)------------------------------
% 14.60/3.69  % (8213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.60/3.69  % (8213)Termination reason: Refutation not found, incomplete strategy
% 14.60/3.69  
% 14.60/3.69  
% 14.60/3.69  % (8213)Memory used [KB]: 7164
% 14.60/3.69  % (8213)Time elapsed: 0.070 s
% 14.60/3.69  % (8213)Instructions burned: 142 (million)
% 14.60/3.69  % (8213)------------------------------
% 14.60/3.69  % (8213)------------------------------
% 15.16/3.71  % (8217)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_7835 for (2979ds/40Mi)
% 15.16/3.73  % (8217)Instruction limit reached!
% 15.16/3.73  % (8217)------------------------------
% 15.16/3.73  % (8217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.16/3.73  % (8217)Termination reason: Unknown
% 15.16/3.73  % (8217)Termination phase: shuffling
% 15.16/3.73  
% 15.16/3.73  % (8217)Memory used [KB]: 2174
% 15.16/3.73  % (8217)Time elapsed: 0.020 s
% 15.16/3.73  % (8217)Instructions burned: 41 (million)
% 15.16/3.73  % (8217)------------------------------
% 15.16/3.73  % (8217)------------------------------
% 15.16/3.75  % (8219)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_7835 for (2979ds/294Mi)
% 15.16/3.78  % (8219)Refutation not found, incomplete strategy
% 15.16/3.78  % (8219)------------------------------
% 15.16/3.78  % (8219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.16/3.78  % (8219)Termination reason: Refutation not found, incomplete strategy
% 15.16/3.78  
% 15.16/3.78  
% 15.16/3.78  % (8219)Memory used [KB]: 6780
% 15.16/3.78  % (8219)Time elapsed: 0.035 s
% 15.16/3.78  % (8219)Instructions burned: 107 (million)
% 15.16/3.78  % (8219)------------------------------
% 15.16/3.78  % (8219)------------------------------
% 15.16/3.79  % (8222)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_7835 for (2978ds/187Mi)
% 15.16/3.80  % (8203)Instruction limit reached!
% 15.16/3.80  % (8203)------------------------------
% 15.16/3.80  % (8203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.16/3.80  % (8203)Termination reason: Unknown
% 15.16/3.80  % (8203)Termination phase: Saturation
% 15.16/3.80  
% 15.16/3.80  % (8203)Memory used [KB]: 8699
% 15.16/3.80  % (8203)Time elapsed: 0.393 s
% 15.16/3.80  % (8203)Instructions burned: 997 (million)
% 15.16/3.80  % (8203)------------------------------
% 15.16/3.80  % (8203)------------------------------
% 15.45/3.80  % (8188)Instruction limit reached!
% 15.45/3.80  % (8188)------------------------------
% 15.45/3.80  % (8188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.45/3.80  % (8188)Termination reason: Unknown
% 15.45/3.80  % (8188)Termination phase: Saturation
% 15.45/3.80  
% 15.45/3.80  % (8188)Memory used [KB]: 5500
% 15.45/3.80  % (8188)Time elapsed: 0.749 s
% 15.45/3.80  % (8188)Instructions burned: 1913 (million)
% 15.45/3.80  % (8188)------------------------------
% 15.45/3.80  % (8188)------------------------------
% 15.45/3.81  % (8223)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7835 for (2978ds/371Mi)
% 15.45/3.81  % (8224)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7835 for (2978ds/1827Mi)
% 15.45/3.84  % (8222)Instruction limit reached!
% 15.45/3.84  % (8222)------------------------------
% 15.45/3.84  % (8222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.45/3.84  % (8222)Termination reason: Unknown
% 15.45/3.84  % (8222)Termination phase: Saturation
% 15.45/3.84  
% 15.45/3.84  % (8222)Memory used [KB]: 7036
% 15.45/3.84  % (8222)Time elapsed: 0.054 s
% 15.45/3.84  % (8222)Instructions burned: 190 (million)
% 15.45/3.84  % (8222)------------------------------
% 15.45/3.84  % (8222)------------------------------
% 15.45/3.85  % (8225)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_7835 for (2978ds/70Mi)
% 15.45/3.87  % (8225)Instruction limit reached!
% 15.45/3.87  % (8225)------------------------------
% 15.45/3.87  % (8225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.45/3.87  % (8225)Termination reason: Unknown
% 15.45/3.87  % (8225)Termination phase: Preprocessing 1
% 15.45/3.87  
% 15.45/3.87  % (8225)Memory used [KB]: 2174
% 15.45/3.87  % (8225)Time elapsed: 0.021 s
% 15.45/3.87  % (8225)Instructions burned: 71 (million)
% 15.45/3.87  % (8225)------------------------------
% 15.45/3.87  % (8225)------------------------------
% 15.45/3.88  % (8226)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_7835 for (2977ds/316Mi)
% 15.45/3.89  % (8216)Instruction limit reached!
% 15.45/3.89  % (8216)------------------------------
% 15.45/3.89  % (8216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.45/3.89  % (8216)Termination reason: Unknown
% 15.45/3.89  % (8216)Termination phase: Saturation
% 15.45/3.89  
% 15.45/3.89  % (8216)Memory used [KB]: 12025
% 15.45/3.89  % (8216)Time elapsed: 0.196 s
% 15.45/3.89  % (8216)Instructions burned: 672 (million)
% 15.45/3.89  % (8216)------------------------------
% 15.45/3.89  % (8216)------------------------------
% 17.11/3.90  % (8230)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_7835 for (2977ds/932Mi)
% 17.11/3.91  % (8223)Instruction limit reached!
% 17.11/3.91  % (8223)------------------------------
% 17.11/3.91  % (8223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.91  % (8223)Termination reason: Unknown
% 17.11/3.91  % (8223)Termination phase: Saturation
% 17.11/3.91  
% 17.11/3.91  % (8223)Memory used [KB]: 7291
% 17.11/3.91  % (8223)Time elapsed: 0.101 s
% 17.11/3.91  % (8223)Instructions burned: 373 (million)
% 17.11/3.91  % (8223)------------------------------
% 17.11/3.91  % (8223)------------------------------
% 17.11/3.92  % (8238)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_7835 for (2977ds/4714Mi)
% 17.11/3.95  % (8226)Refutation not found, incomplete strategy
% 17.11/3.95  % (8226)------------------------------
% 17.11/3.95  % (8226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.95  % (8226)Termination reason: Refutation not found, incomplete strategy
% 17.11/3.95  
% 17.11/3.95  
% 17.11/3.95  % (8226)Memory used [KB]: 7547
% 17.11/3.95  % (8226)Time elapsed: 0.065 s
% 17.11/3.95  % (8226)Instructions burned: 235 (million)
% 17.11/3.95  % (8226)------------------------------
% 17.11/3.95  % (8226)------------------------------
% 17.11/3.96  % (8255)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_7835 for (2977ds/8250Mi)
% 17.11/3.99  % (8238)Refutation not found, incomplete strategy
% 17.11/3.99  % (8238)------------------------------
% 17.11/3.99  % (8238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.99  % (8238)Termination reason: Refutation not found, incomplete strategy
% 17.11/3.99  
% 17.11/3.99  
% 17.11/3.99  % (8238)Memory used [KB]: 7547
% 17.11/3.99  % (8238)Time elapsed: 0.071 s
% 17.11/3.99  % (8238)Instructions burned: 253 (million)
% 17.11/3.99  % (8238)------------------------------
% 17.11/3.99  % (8238)------------------------------
% 17.11/4.00  % (8273)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_7835 for (2976ds/770Mi)
% 17.11/4.01  % (8273)Refutation not found, incomplete strategy
% 17.11/4.01  % (8273)------------------------------
% 17.11/4.01  % (8273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/4.01  % (8273)Termination reason: Refutation not found, incomplete strategy
% 17.11/4.01  
% 17.11/4.01  
% 17.11/4.01  % (8273)Memory used [KB]: 6396
% 17.11/4.01  % (8273)Time elapsed: 0.015 s
% 17.11/4.01  % (8273)Instructions burned: 46 (million)
% 17.11/4.01  % (8273)------------------------------
% 17.11/4.01  % (8273)------------------------------
% 18.86/4.02  % (8284)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_7835 for (2976ds/794Mi)
% 20.01/4.21  % (8230)Instruction limit reached!
% 20.01/4.21  % (8230)------------------------------
% 20.01/4.21  % (8230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.21  % (8230)Termination reason: Unknown
% 20.01/4.21  % (8230)Termination phase: Saturation
% 20.01/4.21  
% 20.01/4.21  % (8230)Memory used [KB]: 9210
% 20.01/4.21  % (8230)Time elapsed: 0.313 s
% 20.01/4.21  % (8230)Instructions burned: 932 (million)
% 20.01/4.21  % (8230)------------------------------
% 20.01/4.21  % (8230)------------------------------
% 20.01/4.22  % (8371)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_7835 for (2974ds/464Mi)
% 20.01/4.27  % (8284)Instruction limit reached!
% 20.01/4.27  % (8284)------------------------------
% 20.01/4.27  % (8284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.27  % (8284)Termination reason: Unknown
% 20.01/4.27  % (8284)Termination phase: Saturation
% 20.01/4.27  
% 20.01/4.27  % (8284)Memory used [KB]: 5245
% 20.01/4.27  % (8284)Time elapsed: 0.249 s
% 20.01/4.27  % (8284)Instructions burned: 795 (million)
% 20.01/4.27  % (8284)------------------------------
% 20.01/4.27  % (8284)------------------------------
% 20.01/4.28  % (8389)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_7835 for (2973ds/1376Mi)
% 20.80/4.35  % (8371)Instruction limit reached!
% 20.80/4.35  % (8371)------------------------------
% 20.80/4.35  % (8371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.80/4.35  % (8371)Termination reason: Unknown
% 20.80/4.35  % (8371)Termination phase: Saturation
% 20.80/4.35  
% 20.80/4.35  % (8371)Memory used [KB]: 7547
% 20.80/4.35  % (8371)Time elapsed: 0.129 s
% 20.80/4.35  % (8371)Instructions burned: 464 (million)
% 20.80/4.35  % (8371)------------------------------
% 20.80/4.35  % (8371)------------------------------
% 20.80/4.36  % (8414)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_7835 for (2973ds/906Mi)
% 20.80/4.39  % (8224)Instruction limit reached!
% 20.80/4.39  % (8224)------------------------------
% 20.80/4.39  % (8224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.80/4.39  % (8224)Termination reason: Unknown
% 20.80/4.39  % (8224)Termination phase: Saturation
% 20.80/4.39  
% 20.80/4.39  % (8224)Memory used [KB]: 10234
% 20.80/4.39  % (8224)Time elapsed: 0.588 s
% 20.80/4.39  % (8224)Instructions burned: 1829 (million)
% 20.80/4.39  % (8224)------------------------------
% 20.80/4.39  % (8224)------------------------------
% 21.44/4.40  % (8428)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_7835 for (2972ds/434Mi)
% 21.44/4.42  % (8428)Refutation not found, incomplete strategy
% 21.44/4.42  % (8428)------------------------------
% 21.44/4.42  % (8428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.42  % (8428)Termination reason: Refutation not found, incomplete strategy
% 21.44/4.42  
% 21.44/4.42  
% 21.44/4.42  % (8428)Memory used [KB]: 6396
% 21.44/4.42  % (8428)Time elapsed: 0.015 s
% 21.44/4.42  % (8428)Instructions burned: 44 (million)
% 21.44/4.42  % (8428)------------------------------
% 21.44/4.42  % (8428)------------------------------
% 21.44/4.43  % (8439)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_7835 for (2972ds/865Mi)
% 21.86/4.52  % (8191)Refutation not found, non-redundant clauses discarded% (8191)------------------------------
% 21.86/4.52  % (8191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.86/4.52  % (8191)Termination reason: Refutation not found, non-redundant clauses discarded
% 21.86/4.52  
% 21.86/4.52  % (8191)Memory used [KB]: 7547
% 21.86/4.52  % (8191)Time elapsed: 1.396 s
% 21.86/4.52  % (8191)Instructions burned: 4052 (million)
% 21.86/4.52  % (8191)------------------------------
% 21.86/4.52  % (8191)------------------------------
% 21.86/4.53  % (8470)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_7835 for (2971ds/593Mi)
% 21.86/4.58  % (8180)Instruction limit reached!
% 21.86/4.58  % (8180)------------------------------
% 21.86/4.58  % (8180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.86/4.58  % (8180)Termination reason: Unknown
% 21.86/4.58  % (8180)Termination phase: Saturation
% 21.86/4.58  
% 21.86/4.58  % (8180)Memory used [KB]: 9978
% 21.86/4.58  % (8180)Time elapsed: 1.712 s
% 21.86/4.58  % (8180)Instructions burned: 4437 (million)
% 21.86/4.58  % (8180)------------------------------
% 21.86/4.58  % (8180)------------------------------
% 21.86/4.59  % (8471)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_7835 for (2970ds/443Mi)
% 22.19/4.65  % (8414)Instruction limit reached!
% 22.19/4.65  % (8414)------------------------------
% 22.19/4.65  % (8414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.65  % (8414)Termination reason: Unknown
% 22.19/4.65  % (8414)Termination phase: Saturation
% 22.19/4.65  
% 22.19/4.65  % (8414)Memory used [KB]: 12153
% 22.19/4.65  % (8414)Time elapsed: 0.297 s
% 22.19/4.65  % (8414)Instructions burned: 908 (million)
% 22.19/4.65  % (8414)------------------------------
% 22.19/4.65  % (8414)------------------------------
% 22.19/4.66  % (8472)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_7835 for (2969ds/594Mi)
% 22.19/4.69  % (8389)Instruction limit reached!
% 22.19/4.69  % (8389)------------------------------
% 22.19/4.69  % (8389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.69  % (8389)Termination reason: Unknown
% 22.19/4.69  % (8389)Termination phase: Saturation
% 22.19/4.69  
% 22.19/4.69  % (8389)Memory used [KB]: 13048
% 22.19/4.69  % (8389)Time elapsed: 0.432 s
% 22.19/4.69  % (8389)Instructions burned: 1377 (million)
% 22.19/4.69  % (8389)------------------------------
% 22.19/4.69  % (8389)------------------------------
% 22.19/4.69  % (8439)Instruction limit reached!
% 22.19/4.69  % (8439)------------------------------
% 22.19/4.69  % (8439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.69  % (8439)Termination reason: Unknown
% 22.19/4.69  % (8439)Termination phase: Saturation
% 22.19/4.69  
% 22.19/4.69  % (8439)Memory used [KB]: 8059
% 22.19/4.69  % (8439)Time elapsed: 0.285 s
% 22.19/4.69  % (8439)Instructions burned: 867 (million)
% 22.19/4.69  % (8439)------------------------------
% 22.19/4.69  % (8439)------------------------------
% 22.19/4.69  % (8470)Instruction limit reached!
% 22.19/4.69  % (8470)------------------------------
% 22.19/4.69  % (8470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.69  % (8470)Termination reason: Unknown
% 22.19/4.69  % (8470)Termination phase: Saturation
% 22.19/4.69  
% 22.19/4.69  % (8470)Memory used [KB]: 7675
% 22.19/4.69  % (8470)Time elapsed: 0.166 s
% 22.19/4.69  % (8470)Instructions burned: 593 (million)
% 22.19/4.69  % (8470)------------------------------
% 22.19/4.69  % (8470)------------------------------
% 23.56/4.70  % (8473)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_7835 for (2969ds/327Mi)
% 23.56/4.70  % (8474)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_7835 for (2969ds/5411Mi)
% 23.56/4.70  % (8475)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_7835 for (2969ds/1762Mi)
% 23.56/4.71  % (8474)Refutation not found, incomplete strategy
% 23.56/4.71  % (8474)------------------------------
% 23.56/4.71  % (8474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.71  % (8474)Termination reason: Refutation not found, incomplete strategy
% 23.56/4.71  
% 23.56/4.71  
% 23.56/4.71  % (8474)Memory used [KB]: 6396
% 23.56/4.71  % (8474)Time elapsed: 0.015 s
% 23.56/4.71  % (8474)Instructions burned: 45 (million)
% 23.56/4.71  % (8474)------------------------------
% 23.56/4.71  % (8474)------------------------------
% 23.56/4.72  % (8471)Instruction limit reached!
% 23.56/4.72  % (8471)------------------------------
% 23.56/4.72  % (8471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.72  % (8471)Termination reason: Unknown
% 23.56/4.72  % (8471)Termination phase: Saturation
% 23.56/4.72  
% 23.56/4.72  % (8471)Memory used [KB]: 7803
% 23.56/4.72  % (8471)Time elapsed: 0.126 s
% 23.56/4.72  % (8471)Instructions burned: 443 (million)
% 23.56/4.72  % (8471)------------------------------
% 23.56/4.72  % (8471)------------------------------
% 23.56/4.72  % (8476)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_7835 for (2969ds/96Mi)
% 23.56/4.73  % (8477)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_7835 for (2969ds/503Mi)
% 23.56/4.74  % (8477)Refutation not found, incomplete strategy
% 23.56/4.74  % (8477)------------------------------
% 23.56/4.74  % (8477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.74  % (8477)Termination reason: Refutation not found, incomplete strategy
% 23.56/4.74  
% 23.56/4.74  
% 23.56/4.74  % (8477)Memory used [KB]: 6396
% 23.56/4.74  % (8477)Time elapsed: 0.016 s
% 23.56/4.74  % (8477)Instructions burned: 46 (million)
% 23.56/4.74  % (8477)------------------------------
% 23.56/4.74  % (8477)------------------------------
% 23.56/4.75  % (8476)Instruction limit reached!
% 23.56/4.75  % (8476)------------------------------
% 23.56/4.75  % (8476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.75  % (8476)Termination reason: Unknown
% 23.56/4.75  % (8476)Termination phase: Property scanning
% 23.56/4.75  
% 23.56/4.75  % (8476)Memory used [KB]: 2302
% 23.56/4.75  % (8476)Time elapsed: 0.028 s
% 23.56/4.75  % (8476)Instructions burned: 99 (million)
% 23.56/4.75  % (8476)------------------------------
% 23.56/4.75  % (8476)------------------------------
% 23.56/4.75  % (8478)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_7835 for (2969ds/90Mi)
% 23.56/4.76  % (8184)Instruction limit reached!
% 23.56/4.76  % (8184)------------------------------
% 23.56/4.76  % (8184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.76  % (8184)Termination reason: Unknown
% 23.56/4.76  % (8184)Termination phase: Saturation
% 23.56/4.76  
% 23.56/4.76  % (8184)Memory used [KB]: 14711
% 23.56/4.76  % (8184)Time elapsed: 1.823 s
% 23.56/4.76  % (8184)Instructions burned: 5207 (million)
% 23.56/4.76  % (8184)------------------------------
% 23.56/4.76  % (8184)------------------------------
% 23.56/4.76  % (8479)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_7835 for (2968ds/593Mi)
% 23.56/4.77  % (8480)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_7835 for (2968ds/1512Mi)
% 23.56/4.78  % (8478)Instruction limit reached!
% 23.56/4.78  % (8478)------------------------------
% 23.56/4.78  % (8478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.78  % (8478)Termination reason: Unknown
% 23.56/4.78  % (8478)Termination phase: Property scanning
% 23.56/4.78  
% 23.56/4.78  % (8478)Memory used [KB]: 2174
% 23.56/4.78  % (8478)Time elapsed: 0.027 s
% 23.56/4.78  % (8478)Instructions burned: 92 (million)
% 23.56/4.78  % (8478)------------------------------
% 23.56/4.78  % (8478)------------------------------
% 23.56/4.79  % (8481)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_7835 for (2968ds/569Mi)
% 24.00/4.80  % (8473)Instruction limit reached!
% 24.00/4.80  % (8473)------------------------------
% 24.00/4.80  % (8473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.80  % (8473)Termination reason: Unknown
% 24.00/4.80  % (8473)Termination phase: Saturation
% 24.00/4.80  
% 24.00/4.80  % (8473)Memory used [KB]: 7547
% 24.00/4.80  % (8473)Time elapsed: 0.105 s
% 24.00/4.80  % (8473)Instructions burned: 329 (million)
% 24.00/4.80  % (8473)------------------------------
% 24.00/4.80  % (8473)------------------------------
% 24.00/4.81  % (8480)Refutation not found, incomplete strategy
% 24.00/4.81  % (8480)------------------------------
% 24.00/4.81  % (8480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.81  % (8480)Termination reason: Refutation not found, incomplete strategy
% 24.00/4.81  
% 24.00/4.81  
% 24.00/4.81  % (8480)Memory used [KB]: 7164
% 24.00/4.81  % (8480)Time elapsed: 0.045 s
% 24.00/4.81  % (8480)Instructions burned: 142 (million)
% 24.00/4.81  % (8480)------------------------------
% 24.00/4.81  % (8480)------------------------------
% 24.00/4.81  % (8482)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_7835 for (2968ds/501Mi)
% 24.00/4.82  % (8483)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_7835 for (2968ds/562Mi)
% 24.00/4.85  % (8472)Instruction limit reached!
% 24.00/4.85  % (8472)------------------------------
% 24.00/4.85  % (8472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.85  % (8472)Termination reason: Unknown
% 24.00/4.85  % (8472)Termination phase: Saturation
% 24.00/4.85  
% 24.00/4.85  % (8472)Memory used [KB]: 8059
% 24.00/4.85  % (8472)Time elapsed: 0.183 s
% 24.00/4.85  % (8472)Instructions burned: 596 (million)
% 24.00/4.85  % (8472)------------------------------
% 24.00/4.85  % (8472)------------------------------
% 24.00/4.86  % (8484)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_7835 for (2968ds/406Mi)
% 24.00/4.87  % (8482)Refutation not found, incomplete strategy
% 24.00/4.87  % (8482)------------------------------
% 24.00/4.87  % (8482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.87  % (8482)Termination reason: Refutation not found, incomplete strategy
% 24.00/4.87  
% 24.00/4.87  
% 24.00/4.87  % (8482)Memory used [KB]: 7419
% 24.00/4.87  % (8482)Time elapsed: 0.056 s
% 24.00/4.87  % (8482)Instructions burned: 191 (million)
% 24.00/4.87  % (8482)------------------------------
% 24.00/4.87  % (8482)------------------------------
% 24.00/4.88  % (8485)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_7835 for (2967ds/582Mi)
% 24.51/4.93  % (8479)Instruction limit reached!
% 24.51/4.93  % (8479)------------------------------
% 24.51/4.93  % (8479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.93  % (8479)Termination reason: Unknown
% 24.51/4.93  % (8479)Termination phase: Saturation
% 24.51/4.93  
% 24.51/4.93  % (8479)Memory used [KB]: 8571
% 24.51/4.93  % (8479)Time elapsed: 0.168 s
% 24.51/4.93  % (8479)Instructions burned: 593 (million)
% 24.51/4.93  % (8479)------------------------------
% 24.51/4.93  % (8479)------------------------------
% 24.51/4.94  % (8486)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_7835 for (2967ds/456Mi)
% 24.51/4.94  % (8481)Instruction limit reached!
% 24.51/4.94  % (8481)------------------------------
% 24.51/4.94  % (8481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.94  % (8481)Termination reason: Unknown
% 24.51/4.94  % (8481)Termination phase: Saturation
% 24.51/4.94  
% 24.51/4.94  % (8481)Memory used [KB]: 7419
% 24.51/4.94  % (8481)Time elapsed: 0.157 s
% 24.51/4.94  % (8481)Instructions burned: 570 (million)
% 24.51/4.94  % (8481)------------------------------
% 24.51/4.94  % (8481)------------------------------
% 24.51/4.95  % (8487)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_7835 for (2967ds/393Mi)
% 24.51/4.98  % (8484)Instruction limit reached!
% 24.51/4.98  % (8484)------------------------------
% 24.51/4.98  % (8484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.98  % (8484)Termination reason: Unknown
% 24.51/4.98  % (8484)Termination phase: Saturation
% 24.51/4.98  
% 24.51/4.98  % (8484)Memory used [KB]: 7803
% 24.51/4.98  % (8484)Time elapsed: 0.129 s
% 24.51/4.98  % (8484)Instructions burned: 407 (million)
% 24.51/4.98  % (8484)------------------------------
% 24.51/4.98  % (8484)------------------------------
% 24.51/4.99  % (8488)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_7835 for (2966ds/1335Mi)
% 24.51/4.99  % (8483)Instruction limit reached!
% 24.51/4.99  % (8483)------------------------------
% 24.51/4.99  % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.99  % (8483)Termination reason: Unknown
% 24.51/4.99  % (8483)Termination phase: Saturation
% 24.51/4.99  
% 24.51/4.99  % (8483)Memory used [KB]: 7675
% 24.51/4.99  % (8483)Time elapsed: 0.175 s
% 24.51/4.99  % (8483)Instructions burned: 563 (million)
% 24.51/4.99  % (8483)------------------------------
% 24.51/4.99  % (8483)------------------------------
% 24.51/5.00  % (8489)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_7835 for (2966ds/3373Mi)
% 25.96/5.04  % (8485)Instruction limit reached!
% 25.96/5.04  % (8485)------------------------------
% 25.96/5.04  % (8485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.96/5.04  % (8485)Termination reason: Unknown
% 25.96/5.04  % (8485)Termination phase: Saturation
% 25.96/5.04  
% 25.96/5.04  % (8485)Memory used [KB]: 8699
% 25.96/5.04  % (8485)Time elapsed: 0.165 s
% 25.96/5.04  % (8485)Instructions burned: 583 (million)
% 25.96/5.04  % (8485)------------------------------
% 25.96/5.04  % (8485)------------------------------
% 25.96/5.05  % (8490)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_7835 for (2966ds/474Mi)
% 25.96/5.06  % (8487)Instruction limit reached!
% 25.96/5.06  % (8487)------------------------------
% 25.96/5.06  % (8487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.96/5.06  % (8487)Termination reason: Unknown
% 25.96/5.06  % (8487)Termination phase: Saturation
% 25.96/5.06  
% 25.96/5.06  % (8487)Memory used [KB]: 7419
% 25.96/5.06  % (8487)Time elapsed: 0.110 s
% 25.96/5.06  % (8487)Instructions burned: 394 (million)
% 25.96/5.06  % (8487)------------------------------
% 25.96/5.06  % (8487)------------------------------
% 25.96/5.07  % (8486)Instruction limit reached!
% 25.96/5.07  % (8486)------------------------------
% 25.96/5.07  % (8486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.96/5.07  % (8486)Termination reason: Unknown
% 25.96/5.07  % (8486)Termination phase: Saturation
% 25.96/5.07  
% 25.96/5.07  % (8486)Memory used [KB]: 7803
% 25.96/5.07  % (8486)Time elapsed: 0.136 s
% 25.96/5.07  % (8486)Instructions burned: 458 (million)
% 25.96/5.07  % (8486)------------------------------
% 25.96/5.07  % (8486)------------------------------
% 25.96/5.07  % (8491)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_7835 for (2965ds/157Mi)
% 25.96/5.08  % (8492)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_7835 for (2965ds/590Mi)
% 25.96/5.11  % (8491)Instruction limit reached!
% 25.96/5.11  % (8491)------------------------------
% 25.96/5.11  % (8491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.96/5.11  % (8491)Termination reason: Unknown
% 25.96/5.11  % (8491)Termination phase: Saturation
% 25.96/5.11  
% 25.96/5.11  % (8491)Memory used [KB]: 2302
% 25.96/5.11  % (8491)Time elapsed: 0.043 s
% 25.96/5.11  % (8491)Instructions burned: 159 (million)
% 25.96/5.11  % (8491)------------------------------
% 25.96/5.11  % (8491)------------------------------
% 25.96/5.12  % (8493)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_7835 for (2965ds/104Mi)
% 26.57/5.15  % (8493)Instruction limit reached!
% 26.57/5.15  % (8493)------------------------------
% 26.57/5.15  % (8493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.57/5.15  % (8493)Termination reason: Unknown
% 26.57/5.15  % (8493)Termination phase: Property scanning
% 26.57/5.15  
% 26.57/5.15  % (8493)Memory used [KB]: 2174
% 26.57/5.15  % (8493)Time elapsed: 0.030 s
% 26.57/5.15  % (8493)Instructions burned: 105 (million)
% 26.57/5.15  % (8493)------------------------------
% 26.57/5.15  % (8493)------------------------------
% 26.57/5.16  % (8494)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_7835 for (2964ds/414Mi)
% 26.57/5.19  % (8490)Instruction limit reached!
% 26.57/5.19  % (8490)------------------------------
% 26.57/5.19  % (8490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.57/5.19  % (8490)Termination reason: Unknown
% 26.57/5.19  % (8490)Termination phase: Saturation
% 26.57/5.19  
% 26.57/5.19  % (8490)Memory used [KB]: 8315
% 26.57/5.19  % (8490)Time elapsed: 0.141 s
% 26.57/5.19  % (8490)Instructions burned: 476 (million)
% 26.57/5.19  % (8490)------------------------------
% 26.57/5.19  % (8490)------------------------------
% 27.04/5.20  % (8495)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_7835 for (2964ds/715Mi)
% 27.04/5.22  % (8475)Instruction limit reached!
% 27.04/5.22  % (8475)------------------------------
% 27.04/5.22  % (8475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.22  % (8475)Termination reason: Unknown
% 27.04/5.22  % (8475)Termination phase: Saturation
% 27.04/5.22  
% 27.04/5.22  % (8475)Memory used [KB]: 10490
% 27.04/5.22  % (8475)Time elapsed: 0.520 s
% 27.04/5.22  % (8475)Instructions burned: 1764 (million)
% 27.04/5.22  % (8475)------------------------------
% 27.04/5.22  % (8475)------------------------------
% 27.04/5.23  % (8496)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_7835 for (2964ds/961Mi)
% 27.04/5.26  % (8492)Instruction limit reached!
% 27.04/5.26  % (8492)------------------------------
% 27.04/5.26  % (8492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.26  % (8492)Termination reason: Unknown
% 27.04/5.26  % (8492)Termination phase: Saturation
% 27.04/5.26  
% 27.04/5.26  % (8492)Memory used [KB]: 6908
% 27.04/5.26  % (8492)Time elapsed: 0.176 s
% 27.04/5.26  % (8492)Instructions burned: 592 (million)
% 27.04/5.26  % (8492)------------------------------
% 27.04/5.26  % (8492)------------------------------
% 27.04/5.27  % (8497)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_7835 for (2963ds/1213Mi)
% 27.04/5.28  % (8494)Instruction limit reached!
% 27.04/5.28  % (8494)------------------------------
% 27.04/5.28  % (8494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.28  % (8494)Termination reason: Unknown
% 27.04/5.28  % (8494)Termination phase: Saturation
% 27.04/5.28  
% 27.04/5.28  % (8494)Memory used [KB]: 7675
% 27.04/5.28  % (8494)Time elapsed: 0.119 s
% 27.04/5.28  % (8494)Instructions burned: 414 (million)
% 27.04/5.28  % (8494)------------------------------
% 27.04/5.28  % (8494)------------------------------
% 27.04/5.29  % (8498)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_7835 for (2963ds/1979Mi)
% 27.70/5.39  % (8488)Instruction limit reached!
% 27.70/5.39  % (8488)------------------------------
% 27.70/5.39  % (8488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.70/5.39  % (8488)Termination reason: Unknown
% 27.70/5.39  % (8488)Termination phase: Saturation
% 27.70/5.39  
% 27.70/5.39  % (8488)Memory used [KB]: 8059
% 27.70/5.39  % (8488)Time elapsed: 0.394 s
% 27.70/5.39  % (8488)Instructions burned: 1335 (million)
% 27.70/5.39  % (8488)------------------------------
% 27.70/5.39  % (8488)------------------------------
% 27.70/5.40  % (8499)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_7835 for (2962ds/481Mi)
% 27.99/5.40  % (8495)Instruction limit reached!
% 27.99/5.40  % (8495)------------------------------
% 27.99/5.40  % (8495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.99/5.40  % (8495)Termination reason: Unknown
% 27.99/5.40  % (8495)Termination phase: Saturation
% 27.99/5.40  
% 27.99/5.40  % (8495)Memory used [KB]: 4349
% 27.99/5.40  % (8495)Time elapsed: 0.200 s
% 27.99/5.40  % (8495)Instructions burned: 716 (million)
% 27.99/5.40  % (8495)------------------------------
% 27.99/5.40  % (8495)------------------------------
% 27.99/5.41  % (8500)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_7835 for (2962ds/783Mi)
% 28.39/5.51  % (8496)Instruction limit reached!
% 28.39/5.51  % (8496)------------------------------
% 28.39/5.51  % (8496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.39/5.51  % (8496)Termination reason: Unknown
% 28.39/5.51  % (8496)Termination phase: Saturation
% 28.39/5.51  
% 28.39/5.51  % (8496)Memory used [KB]: 9083
% 28.39/5.51  % (8496)Time elapsed: 0.282 s
% 28.39/5.51  % (8496)Instructions burned: 962 (million)
% 28.39/5.51  % (8496)------------------------------
% 28.39/5.51  % (8496)------------------------------
% 28.39/5.52  % (8501)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_7835 for (2961ds/432Mi)
% 28.39/5.55  % (8499)Instruction limit reached!
% 28.39/5.55  % (8499)------------------------------
% 28.39/5.55  % (8499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.39/5.55  % (8499)Termination reason: Unknown
% 28.39/5.55  % (8499)Termination phase: Saturation
% 28.39/5.55  
% 28.39/5.55  % (8499)Memory used [KB]: 7931
% 28.39/5.55  % (8499)Time elapsed: 0.152 s
% 28.39/5.55  % (8499)Instructions burned: 482 (million)
% 28.39/5.55  % (8499)------------------------------
% 28.39/5.55  % (8499)------------------------------
% 28.39/5.56  % (8502)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_7835 for (2961ds/1670Mi)
% 29.06/5.65  % (8497)Instruction limit reached!
% 29.06/5.65  % (8497)------------------------------
% 29.06/5.65  % (8497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.65  % (8497)Termination reason: Unknown
% 29.06/5.65  % (8497)Termination phase: Saturation
% 29.06/5.65  
% 29.06/5.65  % (8497)Memory used [KB]: 8827
% 29.06/5.65  % (8497)Time elapsed: 0.382 s
% 29.06/5.65  % (8497)Instructions burned: 1214 (million)
% 29.06/5.65  % (8497)------------------------------
% 29.06/5.65  % (8497)------------------------------
% 29.06/5.65  % (8500)Instruction limit reached!
% 29.06/5.65  % (8500)------------------------------
% 29.06/5.65  % (8500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.65  % (8500)Termination reason: Unknown
% 29.06/5.65  % (8500)Termination phase: Saturation
% 29.06/5.65  
% 29.06/5.65  % (8500)Memory used [KB]: 7675
% 29.06/5.65  % (8500)Time elapsed: 0.241 s
% 29.06/5.65  % (8500)Instructions burned: 783 (million)
% 29.06/5.65  % (8500)------------------------------
% 29.06/5.65  % (8500)------------------------------
% 29.06/5.65  % (8501)Instruction limit reached!
% 29.06/5.65  % (8501)------------------------------
% 29.06/5.65  % (8501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.65  % (8501)Termination reason: Unknown
% 29.06/5.65  % (8501)Termination phase: Saturation
% 29.06/5.65  
% 29.06/5.65  % (8501)Memory used [KB]: 7675
% 29.06/5.65  % (8501)Time elapsed: 0.132 s
% 29.06/5.65  % (8501)Instructions burned: 435 (million)
% 29.06/5.65  % (8501)------------------------------
% 29.06/5.65  % (8501)------------------------------
% 29.06/5.66  % (8503)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_7835 for (2960ds/90Mi)
% 29.06/5.66  % (8504)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_7835 for (2960ds/346Mi)
% 29.06/5.66  % (8505)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_7835 for (2960ds/401Mi)
% 29.06/5.68  % (8503)Instruction limit reached!
% 29.06/5.68  % (8503)------------------------------
% 29.06/5.68  % (8503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/5.68  % (8503)Termination reason: Unknown
% 29.06/5.68  % (8503)Termination phase: Property scanning
% 29.06/5.68  
% 29.06/5.68  % (8503)Memory used [KB]: 2174
% 29.06/5.68  % (8503)Time elapsed: 0.027 s
% 29.06/5.68  % (8503)Instructions burned: 92 (million)
% 29.06/5.68  % (8503)------------------------------
% 29.06/5.68  % (8503)------------------------------
% 29.06/5.69  % (8506)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_7835 for (2959ds/6454Mi)
% 30.07/5.76  % (8504)Instruction limit reached!
% 30.07/5.76  % (8504)------------------------------
% 30.07/5.76  % (8504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.07/5.76  % (8504)Termination reason: Unknown
% 30.07/5.76  % (8504)Termination phase: Saturation
% 30.07/5.76  
% 30.07/5.76  % (8504)Memory used [KB]: 7675
% 30.07/5.76  % (8504)Time elapsed: 0.101 s
% 30.07/5.76  % (8504)Instructions burned: 347 (million)
% 30.07/5.76  % (8504)------------------------------
% 30.07/5.76  % (8504)------------------------------
% 30.07/5.77  % (8507)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_7835 for (2959ds/283Mi)
% 30.07/5.77  % (8505)Instruction limit reached!
% 30.07/5.77  % (8505)------------------------------
% 30.07/5.77  % (8505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.07/5.77  % (8505)Termination reason: Unknown
% 30.07/5.77  % (8505)Termination phase: Saturation
% 30.07/5.77  
% 30.07/5.77  % (8505)Memory used [KB]: 7547
% 30.07/5.77  % (8505)Time elapsed: 0.111 s
% 30.07/5.77  % (8505)Instructions burned: 404 (million)
% 30.07/5.77  % (8505)------------------------------
% 30.07/5.77  % (8505)------------------------------
% 30.07/5.78  % (8508)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_7835 for (2958ds/865Mi)
% 30.07/5.79  % (8498)Instruction limit reached!
% 30.07/5.79  % (8498)------------------------------
% 30.07/5.79  % (8498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.07/5.79  % (8498)Termination reason: Unknown
% 30.07/5.79  % (8498)Termination phase: Saturation
% 30.07/5.79  
% 30.07/5.79  % (8498)Memory used [KB]: 8955
% 30.07/5.79  % (8498)Time elapsed: 0.505 s
% 30.07/5.79  % (8498)Instructions burned: 1981 (million)
% 30.07/5.79  % (8498)------------------------------
% 30.07/5.79  % (8498)------------------------------
% 31.01/5.80  % (8509)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_7835 for (2958ds/4528Mi)
% 31.01/5.82  % (8509)Refutation not found, incomplete strategy
% 31.01/5.82  % (8509)------------------------------
% 31.01/5.82  % (8509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/5.82  % (8509)Termination reason: Refutation not found, incomplete strategy
% 31.01/5.82  
% 31.01/5.82  
% 31.01/5.82  % (8509)Memory used [KB]: 1918
% 31.01/5.82  % (8509)Time elapsed: 0.016 s
% 31.01/5.82  % (8509)Instructions burned: 47 (million)
% 31.01/5.82  % (8509)------------------------------
% 31.01/5.82  % (8509)------------------------------
% 31.01/5.83  % (8510)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_7835 for (2958ds/1001Mi)
% 31.01/5.85  % (8507)Instruction limit reached!
% 31.01/5.85  % (8507)------------------------------
% 31.01/5.85  % (8507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/5.85  % (8507)Termination reason: Unknown
% 31.01/5.85  % (8507)Termination phase: Saturation
% 31.01/5.85  
% 31.01/5.85  % (8507)Memory used [KB]: 7419
% 31.01/5.85  % (8507)Time elapsed: 0.083 s
% 31.01/5.85  % (8507)Instructions burned: 284 (million)
% 31.01/5.85  % (8507)------------------------------
% 31.01/5.85  % (8507)------------------------------
% 31.01/5.86  % (8511)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_7835 for (2958ds/102Mi)
% 31.01/5.89  % (8511)Instruction limit reached!
% 31.01/5.89  % (8511)------------------------------
% 31.01/5.89  % (8511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/5.89  % (8511)Termination reason: Unknown
% 31.01/5.89  % (8511)Termination phase: Property scanning
% 31.01/5.89  
% 31.01/5.89  % (8511)Memory used [KB]: 2302
% 31.01/5.89  % (8511)Time elapsed: 0.028 s
% 31.01/5.89  % (8511)Instructions burned: 103 (million)
% 31.01/5.89  % (8511)------------------------------
% 31.01/5.89  % (8511)------------------------------
% 31.01/5.90  % (8512)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_7835 for (2957ds/952Mi)
% 31.37/5.99  % (8502)Instruction limit reached!
% 31.37/5.99  % (8502)------------------------------
% 31.37/5.99  % (8502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.37/5.99  % (8502)Termination reason: Unknown
% 31.37/5.99  % (8502)Termination phase: Saturation
% 31.37/5.99  
% 31.37/5.99  % (8502)Memory used [KB]: 7931
% 31.37/5.99  % (8502)Time elapsed: 0.436 s
% 31.37/5.99  % (8502)Instructions burned: 1673 (million)
% 31.37/5.99  % (8502)------------------------------
% 31.37/5.99  % (8502)------------------------------
% 31.37/6.00  % (8513)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_7835 for (2956ds/578Mi)
% 32.98/6.05  % (8508)Instruction limit reached!
% 32.98/6.05  % (8508)------------------------------
% 32.98/6.05  % (8508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.98/6.05  % (8508)Termination reason: Unknown
% 32.98/6.05  % (8508)Termination phase: Saturation
% 32.98/6.05  
% 32.98/6.05  % (8508)Memory used [KB]: 9083
% 32.98/6.05  % (8508)Time elapsed: 0.270 s
% 32.98/6.05  % (8508)Instructions burned: 866 (million)
% 32.98/6.05  % (8508)------------------------------
% 32.98/6.05  % (8508)------------------------------
% 32.98/6.05  % (8489)Instruction limit reached!
% 32.98/6.05  % (8489)------------------------------
% 32.98/6.05  % (8489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.98/6.05  % (8489)Termination reason: Unknown
% 32.98/6.05  % (8489)Termination phase: Saturation
% 32.98/6.05  
% 32.98/6.05  % (8489)Memory used [KB]: 12025
% 32.98/6.05  % (8489)Time elapsed: 1.050 s
% 32.98/6.05  % (8489)Instructions burned: 3374 (million)
% 32.98/6.05  % (8489)------------------------------
% 32.98/6.05  % (8489)------------------------------
% 32.98/6.06  % (8514)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_7835 for (2956ds/643Mi)
% 32.98/6.06  % (8515)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_7835 for (2955ds/865Mi)
% 33.57/6.13  % (8510)Instruction limit reached!
% 33.57/6.13  % (8510)------------------------------
% 33.57/6.13  % (8510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.57/6.13  % (8510)Termination reason: Unknown
% 33.57/6.13  % (8510)Termination phase: Saturation
% 33.57/6.13  
% 33.57/6.13  % (8510)Memory used [KB]: 9594
% 33.57/6.13  % (8510)Time elapsed: 0.302 s
% 33.57/6.13  % (8510)Instructions burned: 1001 (million)
% 33.57/6.13  % (8510)------------------------------
% 33.57/6.13  % (8510)------------------------------
% 33.57/6.14  % (8516)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_7835 for (2955ds/1174Mi)
% 33.57/6.16  % (8512)Instruction limit reached!
% 33.57/6.16  % (8512)------------------------------
% 33.57/6.16  % (8512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.57/6.16  % (8512)Termination reason: Unknown
% 33.57/6.16  % (8512)Termination phase: Saturation
% 33.57/6.16  
% 33.57/6.16  % (8512)Memory used [KB]: 9210
% 33.57/6.16  % (8512)Time elapsed: 0.264 s
% 33.57/6.16  % (8512)Instructions burned: 954 (million)
% 33.57/6.16  % (8512)------------------------------
% 33.57/6.16  % (8512)------------------------------
% 33.57/6.17  % (8517)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_7835 for (2954ds/644Mi)
% 33.57/6.17  % (8513)Instruction limit reached!
% 33.57/6.17  % (8513)------------------------------
% 33.57/6.17  % (8513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.57/6.17  % (8513)Termination reason: Unknown
% 33.57/6.17  % (8513)Termination phase: Saturation
% 33.57/6.17  
% 33.57/6.17  % (8513)Memory used [KB]: 8571
% 33.57/6.17  % (8513)Time elapsed: 0.195 s
% 33.57/6.17  % (8513)Instructions burned: 580 (million)
% 33.57/6.17  % (8513)------------------------------
% 33.57/6.17  % (8513)------------------------------
% 33.57/6.18  % (8518)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_7835 for (2954ds/1201Mi)
% 33.84/6.24  % (8514)Instruction limit reached!
% 33.84/6.24  % (8514)------------------------------
% 33.84/6.24  % (8514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.84/6.24  % (8514)Termination reason: Unknown
% 33.84/6.24  % (8514)Termination phase: Saturation
% 33.84/6.24  
% 33.84/6.24  % (8514)Memory used [KB]: 8059
% 33.84/6.24  % (8514)Time elapsed: 0.180 s
% 33.84/6.24  % (8514)Instructions burned: 643 (million)
% 33.84/6.24  % (8514)------------------------------
% 33.84/6.24  % (8514)------------------------------
% 33.84/6.25  % (8519)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_7835 for (2954ds/1046Mi)
% 33.84/6.27  % (8515)Refutation not found, non-redundant clauses discarded% (8515)------------------------------
% 33.84/6.27  % (8515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.84/6.27  % (8515)Termination reason: Refutation not found, non-redundant clauses discarded
% 33.84/6.27  
% 33.84/6.27  % (8515)Memory used [KB]: 8059
% 33.84/6.27  % (8515)Time elapsed: 0.212 s
% 33.84/6.27  % (8515)Instructions burned: 679 (million)
% 33.84/6.27  % (8515)------------------------------
% 33.84/6.27  % (8515)------------------------------
% 33.84/6.28  % (8520)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_7835 for (2953ds/222Mi)
% 34.44/6.34  % (8520)Instruction limit reached!
% 34.44/6.34  % (8520)------------------------------
% 34.44/6.34  % (8520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.44/6.34  % (8520)Termination reason: Unknown
% 34.44/6.34  % (8520)Termination phase: Saturation
% 34.44/6.34  
% 34.44/6.34  % (8520)Memory used [KB]: 7164
% 34.44/6.34  % (8520)Time elapsed: 0.060 s
% 34.44/6.34  % (8520)Instructions burned: 223 (million)
% 34.44/6.34  % (8520)------------------------------
% 34.44/6.34  % (8520)------------------------------
% 34.44/6.35  % (8521)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_7835 for (2953ds/68Mi)
% 34.44/6.37  % (8517)Instruction limit reached!
% 34.44/6.37  % (8517)------------------------------
% 34.44/6.37  % (8517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.44/6.37  % (8517)Termination reason: Unknown
% 34.44/6.37  % (8517)Termination phase: Saturation
% 34.44/6.37  
% 34.44/6.37  % (8517)Memory used [KB]: 8699
% 34.44/6.37  % (8517)Time elapsed: 0.204 s
% 34.44/6.37  % (8517)Instructions burned: 644 (million)
% 34.44/6.37  % (8517)------------------------------
% 34.44/6.37  % (8517)------------------------------
% 34.44/6.37  % (8521)Instruction limit reached!
% 34.44/6.37  % (8521)------------------------------
% 34.44/6.37  % (8521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.44/6.37  % (8521)Termination reason: Unknown
% 34.44/6.37  % (8521)Termination phase: Property scanning
% 34.44/6.37  
% 34.44/6.37  % (8521)Memory used [KB]: 2174
% 34.44/6.37  % (8521)Time elapsed: 0.022 s
% 34.44/6.37  % (8521)Instructions burned: 70 (million)
% 34.44/6.37  % (8521)------------------------------
% 34.44/6.37  % (8521)------------------------------
% 34.44/6.38  % (8522)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_7835 for (2952ds/454Mi)
% 34.44/6.38  % (8523)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_7835 for (2952ds/360Mi)
% 34.97/6.48  % (8523)Instruction limit reached!
% 34.97/6.48  % (8523)------------------------------
% 34.97/6.48  % (8523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.48  % (8523)Termination reason: Unknown
% 34.97/6.48  % (8523)Termination phase: Saturation
% 34.97/6.48  
% 34.97/6.48  % (8523)Memory used [KB]: 7291
% 34.97/6.48  % (8523)Time elapsed: 0.099 s
% 34.97/6.48  % (8523)Instructions burned: 360 (million)
% 34.97/6.48  % (8523)------------------------------
% 34.97/6.48  % (8523)------------------------------
% 34.97/6.49  % (8516)First to succeed.
% 34.97/6.49  % (8516)Refutation found. Thanks to Tanya!
% 34.97/6.49  % SZS status Theorem for DTF2THF_7835
% 34.97/6.49  % SZS output start Proof for DTF2THF_7835
% 34.97/6.49  thf(type_def_6, type, secrecy_specID: $tType).
% 34.97/6.49  thf(type_def_7, type, secrecy_Expression: $tType).
% 34.97/6.49  thf(type_def_8, type, secrecy_chanID: $tType).
% 34.97/6.49  thf(type_def_9, type, set: ($tType) > $tType).
% 34.97/6.49  thf(type_def_10, type, nat: $tType).
% 34.97/6.49  thf(func_def_0, type, secrecy_Expression: $tType).
% 34.97/6.49  thf(func_def_1, type, secrecy_specID: $tType).
% 34.97/6.49  thf(func_def_2, type, secrecy_chanID: $tType).
% 34.97/6.49  thf(func_def_3, type, set: ($tType) > $tType).
% 34.97/6.49  thf(func_def_4, type, nat: $tType).
% 34.97/6.49  thf(func_def_5, type, bounded_lattice: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_7, type, bot: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_10, type, lattice: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_13, type, order_bot: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_15, type, semilattice_inf: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_16, type, semilattice_sup: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_17, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_18, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 34.97/6.49  thf(func_def_19, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 34.97/6.49  thf(func_def_20, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 34.97/6.49  thf(func_def_21, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 34.97/6.49  thf(func_def_22, type, bot_bot: !>[X0: $tType]:(X0)).
% 34.97/6.49  thf(func_def_23, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 34.97/6.49  thf(func_def_24, type, eout: secrecy_specID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_25, type, eoutM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_26, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_27, type, ine: secrecy_specID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_28, type, ineM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_29, type, ine_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_30, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_31, type, out_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_32, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 34.97/6.49  thf(func_def_33, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 34.97/6.49  thf(func_def_34, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 34.97/6.49  thf(func_def_35, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 34.97/6.49  thf(func_def_36, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 34.97/6.49  thf(func_def_37, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 34.97/6.49  thf(func_def_38, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_39, type, correctCompositionIn: secrecy_specID > $o).
% 34.97/6.49  thf(func_def_40, type, correc965049635ionLoc: secrecy_specID > $o).
% 34.97/6.49  thf(func_def_41, type, correc990227761ionOut: secrecy_specID > $o).
% 34.97/6.49  thf(func_def_42, type, correctInOutLoc: secrecy_specID > $o).
% 34.97/6.49  thf(func_def_43, type, inStream: secrecy_specID > set @ secrecy_chanID > $o).
% 34.97/6.49  thf(func_def_44, type, ins: secrecy_specID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_45, type, loc: secrecy_specID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_46, type, locStream: secrecy_specID > set @ secrecy_chanID > $o).
% 34.97/6.49  thf(func_def_47, type, out: secrecy_specID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_48, type, outStream: secrecy_specID > set @ secrecy_chanID > $o).
% 34.97/6.49  thf(func_def_49, type, subcomponents: secrecy_specID > set @ secrecy_specID).
% 34.97/6.49  thf(func_def_50, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 34.97/6.49  thf(func_def_51, type, p: secrecy_specID).
% 34.97/6.49  thf(func_def_52, type, pq: secrecy_specID).
% 34.97/6.49  thf(func_def_53, type, q: secrecy_specID).
% 34.97/6.49  thf(func_def_54, type, ch: secrecy_chanID).
% 34.97/6.49  thf(func_def_55, type, m: secrecy_Expression).
% 34.97/6.49  thf(func_def_71, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 34.97/6.49  thf(func_def_72, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 34.97/6.49  thf(func_def_73, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 34.97/6.49  thf(func_def_74, type, sK3: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_75, type, sK4: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_76, type, sK5: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_77, type, sK6: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_78, type, sK7: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_79, type, sK8: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_80, type, sK9: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_81, type, sK10: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_82, type, sK11: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_83, type, sK12: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_84, type, sK13: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 34.97/6.49  thf(func_def_85, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_86, type, sK15: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_87, type, sK16: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_88, type, sK17: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_89, type, sK18: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_90, type, sK19: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_91, type, sK20: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_92, type, sK21: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_93, type, sK22: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_94, type, sK23: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_95, type, sK24: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 34.97/6.49  thf(func_def_96, type, sK25: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 34.97/6.49  thf(func_def_97, type, sK26: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_98, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_99, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_100, type, sK29: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_101, type, sK30: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > X0)).
% 34.97/6.49  thf(func_def_102, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > X0)).
% 34.97/6.49  thf(func_def_103, type, sK32: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_104, type, sK33: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_105, type, sK34: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_106, type, sK35: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_107, type, sK36: !>[X0: $tType]:(set @ X0 > X0)).
% 34.97/6.49  thf(func_def_108, type, sK37: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 34.97/6.49  thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 34.97/6.49  thf(func_def_111, type, sK40: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 34.97/6.49  thf(func_def_112, type, sK41: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 34.97/6.49  thf(func_def_113, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_114, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 34.97/6.49  thf(func_def_115, type, sK44: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 34.97/6.49  thf(func_def_116, type, sK45: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_117, type, sK46: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_118, type, sK47: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_119, type, sK48: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_120, type, sK49: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 34.97/6.49  thf(func_def_121, type, sK50: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 34.97/6.49  thf(func_def_122, type, sK51: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 34.97/6.49  thf(func_def_124, type, ph53: !>[X0: $tType]:(X0)).
% 34.97/6.49  thf(func_def_125, type, sK54: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_126, type, sK55: set @ secrecy_chanID > secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_127, type, sK56: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_128, type, sK57: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_129, type, sK58: set @ secrecy_chanID > secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_130, type, sK59: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_131, type, sK60: set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_132, type, sK61: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_133, type, sK62: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_134, type, sK63: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_135, type, sK64: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_136, type, sK65: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_137, type, sK66: set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_138, type, sK67: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_139, type, sK68: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_140, type, sK69: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_141, type, sK70: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_142, type, sK71: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_143, type, sK72: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_144, type, sK73: set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_145, type, sK74: set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_146, type, sK75: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_147, type, sK76: secrecy_chanID > secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_148, type, sK77: secrecy_chanID > secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_149, type, sK78: set @ set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_150, type, sK79: set @ set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_151, type, sK80: secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_152, type, sK81: secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_153, type, sK82: secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_154, type, sK83: secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID > set @ secrecy_chanID).
% 34.97/6.49  thf(func_def_155, type, sK84: set @ secrecy_specID > secrecy_specID).
% 34.97/6.49  thf(func_def_156, type, sK85: set @ secrecy_specID > secrecy_specID).
% 34.97/6.49  thf(func_def_157, type, sK86: set @ secrecy_specID > secrecy_specID).
% 34.97/6.49  thf(func_def_158, type, sK87: secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_159, type, sK88: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_160, type, sK89: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_161, type, sK90: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_162, type, sK91: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_163, type, sK92: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_164, type, sK93: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_165, type, sK94: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_166, type, sK95: secrecy_Expression > set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_167, type, sK96: secrecy_specID > secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_168, type, sK97: secrecy_specID > secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_169, type, sK98: secrecy_specID > secrecy_Expression > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_170, type, sK99: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_171, type, sK100: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_172, type, sK101: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_173, type, sK102: (secrecy_chanID > secrecy_chanID > $o) > secrecy_chanID).
% 34.97/6.49  thf(func_def_174, type, sK103: (secrecy_chanID > secrecy_chanID > $o) > secrecy_chanID).
% 34.97/6.49  thf(func_def_175, type, sK104: secrecy_Expression > secrecy_specID > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_176, type, sK105: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_177, type, sK106: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_178, type, sK107: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_179, type, sK108: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_180, type, sK109: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_181, type, sK110: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_182, type, sK111: set @ secrecy_chanID > secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_183, type, sK112: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_184, type, sK113: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_185, type, sK114: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_186, type, sK115: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_187, type, sK116: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_188, type, sK117: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_189, type, sK118: (secrecy_chanID > secrecy_chanID > $o) > secrecy_chanID).
% 34.97/6.49  thf(func_def_190, type, sK119: (secrecy_chanID > secrecy_chanID > $o) > secrecy_chanID).
% 34.97/6.49  thf(func_def_191, type, sK120: secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_192, type, sK121: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_193, type, sK122: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_194, type, sK123: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_195, type, sK124: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_196, type, sK125: secrecy_Expression > secrecy_specID > set @ secrecy_chanID > secrecy_chanID).
% 34.97/6.49  thf(func_def_197, type, sK126: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_198, type, sK127: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_199, type, sK128: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_200, type, sK129: set @ secrecy_chanID > secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_201, type, sK130: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_202, type, sK131: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_203, type, sK132: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 34.97/6.49  thf(func_def_204, type, sK133: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(func_def_205, type, sK134: secrecy_specID > secrecy_Expression > secrecy_chanID).
% 34.97/6.49  thf(f4140,plain,(
% 34.97/6.49    $false),
% 34.97/6.49    inference(avatar_sat_refutation,[status(thm)],[f2246,f3262,f4138])).
% 34.97/6.49  thf(f4138,plain,(
% 34.97/6.49    ~spl52_1),
% 34.97/6.49    inference(avatar_contradiction_clause,[status(thm)],[f4137])).
% 34.97/6.49  thf(f4137,plain,(
% 34.97/6.49    $false | ~spl52_1),
% 34.97/6.49    inference(subsumption_resolution,[status(thm)],[f3593,f1358])).
% 34.97/6.49  thf(f1358,plain,(
% 34.97/6.49    ((exprChannel @ ch @ m) = $true)),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f387])).
% 34.97/6.49  thf(f387,plain,(
% 34.97/6.49    ((exprChannel @ ch @ m) = $true)),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f386])).
% 34.97/6.49  thf(f386,plain,(
% 34.97/6.49    (exprChannel @ ch @ m)),
% 34.97/6.49    inference(rectify,[status(thm)],[f2])).
% 34.97/6.49  thf(f2,axiom,(
% 34.97/6.49    (exprChannel @ ch @ m)),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_1_assms_I4_J)).
% 34.97/6.49  thf(f3593,plain,(
% 34.97/6.49    ((exprChannel @ ch @ m) != $true) | ~spl52_1),
% 34.97/6.49    inference(trivial_inequality_removal,[status(thm)],[f3263])).
% 34.97/6.49  thf(f3263,plain,(
% 34.97/6.49    ($true != $true) | ((exprChannel @ ch @ m) != $true) | ~spl52_1),
% 34.97/6.49    inference(superposition,[status(thm)],[f1425,f2242])).
% 34.97/6.49  thf(f2242,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (ins @ pq)) = $true) | ~spl52_1),
% 34.97/6.49    inference(avatar_component_clause,[status(thm)],[f2240])).
% 34.97/6.49  thf(f2240,definition,(
% 34.97/6.49    spl52_1 <=> ((member @ secrecy_chanID @ ch @ (ins @ pq)) = $true)),
% 34.97/6.49    introduced(definition,[new_symbols(naming,[spl52_1])],[avatar_definition])).
% 34.97/6.49  thf(f1425,plain,(
% 34.97/6.49    ( ! [X0 : secrecy_chanID] : (($true != (member @ secrecy_chanID @ X0 @ (ins @ pq))) | ((exprChannel @ X0 @ m) != $true)) )),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f1020])).
% 34.97/6.49  thf(f1020,plain,(
% 34.97/6.49    ! [X0 : secrecy_chanID] : (($true != (member @ secrecy_chanID @ X0 @ (ins @ pq))) | ((exprChannel @ X0 @ m) != $true))),
% 34.97/6.49    inference(ennf_transformation,[status(thm)],[f881])).
% 34.97/6.49  thf(f881,plain,(
% 34.97/6.49    ! [X0 : secrecy_chanID] : (($true = (member @ secrecy_chanID @ X0 @ (ins @ pq))) => ((exprChannel @ X0 @ m) != $true))),
% 34.97/6.49    inference(flattening,[status(thm)],[f349])).
% 34.97/6.49  thf(f349,plain,(
% 34.97/6.49    ! [X0 : secrecy_chanID] : (($true = (member @ secrecy_chanID @ X0 @ (ins @ pq))) => ~((exprChannel @ X0 @ m) = $true))),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f348])).
% 34.97/6.49  thf(f348,plain,(
% 34.97/6.49    ! [X0 : secrecy_chanID] : ((member @ secrecy_chanID @ X0 @ (ins @ pq)) => ~(exprChannel @ X0 @ m))),
% 34.97/6.49    inference(rectify,[status(thm)],[f4])).
% 34.97/6.49  thf(f4,axiom,(
% 34.97/6.49    ! [X1 : secrecy_chanID] : ((member @ secrecy_chanID @ X1 @ (ins @ pq)) => ~(exprChannel @ X1 @ m))),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_3_assms_I5_J)).
% 34.97/6.49  thf(f3262,plain,(
% 34.97/6.49    ~spl52_2),
% 34.97/6.49    inference(avatar_contradiction_clause,[status(thm)],[f3261])).
% 34.97/6.49  thf(f3261,plain,(
% 34.97/6.49    $false | ~spl52_2),
% 34.97/6.49    inference(subsumption_resolution,[status(thm)],[f3247,f1588])).
% 34.97/6.49  thf(f1588,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (ins @ p)) = $true)),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f311])).
% 34.97/6.49  thf(f311,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (ins @ p)) = $true)),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f310])).
% 34.97/6.49  thf(f310,plain,(
% 34.97/6.49    (member @ secrecy_chanID @ ch @ (ins @ p))),
% 34.97/6.49    inference(rectify,[status(thm)],[f3])).
% 34.97/6.49  thf(f3,axiom,(
% 34.97/6.49    (member @ secrecy_chanID @ ch @ (ins @ p))),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_2_assms_I3_J)).
% 34.97/6.49  thf(f3247,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (ins @ p)) != $true) | ~spl52_2),
% 34.97/6.49    inference(trivial_inequality_removal,[status(thm)],[f3242])).
% 34.97/6.49  thf(f3242,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (ins @ p)) != $true) | ((subcomponents @ pq) != (subcomponents @ pq)) | ~spl52_2),
% 34.97/6.49    inference(superposition,[status(thm)],[f2245,f1362])).
% 34.97/6.49  thf(f1362,plain,(
% 34.97/6.49    ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f5])).
% 34.97/6.49  thf(f5,axiom,(
% 34.97/6.49    ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_4_assms_I1_J)).
% 34.97/6.49  thf(f2245,plain,(
% 34.97/6.49    ( ! [X0 : secrecy_specID,X1 : secrecy_specID] : (((subcomponents @ pq) != (insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID))) | ((member @ secrecy_chanID @ ch @ (ins @ X0)) != $true)) ) | ~spl52_2),
% 34.97/6.49    inference(avatar_component_clause,[status(thm)],[f2244])).
% 34.97/6.49  thf(f2244,definition,(
% 34.97/6.49    spl52_2 <=> ! [X0 : secrecy_specID,X1 : secrecy_specID] : (((member @ secrecy_chanID @ ch @ (ins @ X0)) != $true) | ((subcomponents @ pq) != (insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID))))),
% 34.97/6.49    introduced(definition,[new_symbols(naming,[spl52_2])],[avatar_definition])).
% 34.97/6.49  thf(f2246,plain,(
% 34.97/6.49    spl52_1 | spl52_2),
% 34.97/6.49    inference(avatar_split_clause,[status(thm)],[f2238,f2244,f2240])).
% 34.97/6.49  thf(f2238,plain,(
% 34.97/6.49    ( ! [X0 : secrecy_specID,X1 : secrecy_specID] : (((member @ secrecy_chanID @ ch @ (ins @ pq)) = $true) | ((member @ secrecy_chanID @ ch @ (ins @ X0)) != $true) | ((subcomponents @ pq) != (insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))) )),
% 34.97/6.49    inference(subsumption_resolution,[status(thm)],[f2206,f1426])).
% 34.97/6.49  thf(f1426,plain,(
% 34.97/6.49    ((correctCompositionIn @ pq) = $true)),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f391])).
% 34.97/6.49  thf(f391,plain,(
% 34.97/6.49    ((correctCompositionIn @ pq) = $true)),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f390])).
% 34.97/6.49  thf(f390,plain,(
% 34.97/6.49    (correctCompositionIn @ pq)),
% 34.97/6.49    inference(rectify,[status(thm)],[f1])).
% 34.97/6.49  thf(f1,axiom,(
% 34.97/6.49    (correctCompositionIn @ pq)),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_0_assms_I2_J)).
% 34.97/6.49  thf(f2206,plain,(
% 34.97/6.49    ( ! [X0 : secrecy_specID,X1 : secrecy_specID] : (((member @ secrecy_chanID @ ch @ (ins @ X0)) != $true) | ((correctCompositionIn @ pq) != $true) | ((subcomponents @ pq) != (insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID))) | ((member @ secrecy_chanID @ ch @ (ins @ pq)) = $true)) )),
% 34.97/6.49    inference(trivial_inequality_removal,[status(thm)],[f1835])).
% 34.97/6.49  thf(f1835,plain,(
% 34.97/6.49    ( ! [X0 : secrecy_specID,X1 : secrecy_specID] : (((correctCompositionIn @ pq) != $true) | ((member @ secrecy_chanID @ ch @ (ins @ X0)) != $true) | ($true != $true) | ((member @ secrecy_chanID @ ch @ (ins @ pq)) = $true) | ((subcomponents @ pq) != (insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))) )),
% 34.97/6.49    inference(superposition,[status(thm)],[f1539,f1365])).
% 34.97/6.49  thf(f1365,plain,(
% 34.97/6.49    ( ! [X2 : secrecy_specID,X3 : secrecy_chanID,X0 : secrecy_specID,X1 : secrecy_specID] : (($true = (member @ secrecy_chanID @ X3 @ (ins @ X0))) | ((member @ secrecy_chanID @ X3 @ (loc @ X0)) = $true) | ((correctCompositionIn @ X0) != $true) | ((member @ secrecy_chanID @ X3 @ (ins @ X1)) != $true) | ((subcomponents @ X0) != (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)))) )),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f1022])).
% 34.97/6.49  thf(f1022,plain,(
% 34.97/6.49    ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_chanID] : (((member @ secrecy_chanID @ X3 @ (ins @ X1)) != $true) | ($true = (member @ secrecy_chanID @ X3 @ (ins @ X0))) | ((subcomponents @ X0) != (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID))) | ((correctCompositionIn @ X0) != $true) | ((member @ secrecy_chanID @ X3 @ (loc @ X0)) = $true))),
% 34.97/6.49    inference(flattening,[status(thm)],[f1021])).
% 34.97/6.49  thf(f1021,plain,(
% 34.97/6.49    ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_chanID] : ((((($true = (member @ secrecy_chanID @ X3 @ (ins @ X0))) | ((member @ secrecy_chanID @ X3 @ (ins @ X1)) != $true)) | ((member @ secrecy_chanID @ X3 @ (loc @ X0)) = $true)) | ((correctCompositionIn @ X0) != $true)) | ((subcomponents @ X0) != (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID))))),
% 34.97/6.49    inference(ennf_transformation,[status(thm)],[f928])).
% 34.97/6.49  thf(f928,plain,(
% 34.97/6.49    ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_chanID] : (((subcomponents @ X0) = (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID))) => (((correctCompositionIn @ X0) = $true) => (((member @ secrecy_chanID @ X3 @ (loc @ X0)) != $true) => (((member @ secrecy_chanID @ X3 @ (ins @ X1)) = $true) => ($true = (member @ secrecy_chanID @ X3 @ (ins @ X0)))))))),
% 34.97/6.49    inference(flattening,[status(thm)],[f757])).
% 34.97/6.49  thf(f757,plain,(
% 34.97/6.49    ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_chanID] : (((subcomponents @ X0) = (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID))) => (((correctCompositionIn @ X0) = $true) => (~((member @ secrecy_chanID @ X3 @ (loc @ X0)) = $true) => (((member @ secrecy_chanID @ X3 @ (ins @ X1)) = $true) => ($true = (member @ secrecy_chanID @ X3 @ (ins @ X0)))))))),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f756])).
% 34.97/6.49  thf(f756,plain,(
% 34.97/6.49    ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_chanID] : (((subcomponents @ X0) = (insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID))) => ((correctCompositionIn @ X0) => (~(member @ secrecy_chanID @ X3 @ (loc @ X0)) => ((member @ secrecy_chanID @ X3 @ (ins @ X1)) => (member @ secrecy_chanID @ X3 @ (ins @ X0))))))),
% 34.97/6.49    inference(rectify,[status(thm)],[f7])).
% 34.97/6.49  thf(f7,axiom,(
% 34.97/6.49    ! [X5 : secrecy_specID,X6 : secrecy_specID,X7 : secrecy_specID,X8 : secrecy_chanID] : (((subcomponents @ X5) = (insert @ secrecy_specID @ X6 @ (insert @ secrecy_specID @ X7 @ bot_bot @ set @ secrecy_specID))) => ((correctCompositionIn @ X5) => (~(member @ secrecy_chanID @ X8 @ (loc @ X5)) => ((member @ secrecy_chanID @ X8 @ (ins @ X6)) => (member @ secrecy_chanID @ X8 @ (ins @ X5))))))),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',fact_6_correctCompositionIn__L1)).
% 34.97/6.49  thf(f1539,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (loc @ pq)) != $true)),
% 34.97/6.49    inference(cnf_transformation,[status(thm)],[f897])).
% 34.97/6.49  thf(f897,plain,(
% 34.97/6.49    ((member @ secrecy_chanID @ ch @ (loc @ pq)) != $true)),
% 34.97/6.49    inference(flattening,[status(thm)],[f503])).
% 34.97/6.49  thf(f503,plain,(
% 34.97/6.49    ~((member @ secrecy_chanID @ ch @ (loc @ pq)) = $true)),
% 34.97/6.49    inference(fool_elimination,[status(thm)],[f502])).
% 34.97/6.49  thf(f502,plain,(
% 34.97/6.49    ~(member @ secrecy_chanID @ ch @ (loc @ pq))),
% 34.97/6.49    inference(rectify,[status(thm)],[f304])).
% 34.97/6.49  thf(f304,negated_conjecture,(
% 34.97/6.49    ~(member @ secrecy_chanID @ ch @ (loc @ pq))),
% 34.97/6.49    inference(negated_conjecture,[status(cth)],[f303])).
% 34.97/6.49  thf(f303,conjecture,(
% 34.97/6.49    (member @ secrecy_chanID @ ch @ (loc @ pq))),
% 34.97/6.49    file('/export/starexec/sandbox2/tmp/tmp.XG27T5VWLw/DTF2THF_7835.p',conj_0)).
% 34.97/6.49  % SZS output end Proof for DTF2THF_7835
% 34.97/6.49  % (8516)------------------------------
% 34.97/6.49  % (8516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.49  % (8516)Termination reason: Refutation
% 34.97/6.49  
% 34.97/6.49  % (8516)Memory used [KB]: 9338
% 34.97/6.49  % (8516)Time elapsed: 0.350 s
% 34.97/6.49  % (8516)Instructions burned: 1132 (million)
% 34.97/6.49  % (8516)------------------------------
% 34.97/6.49  % (8516)------------------------------
% 34.97/6.49  % (8017)Success in time 4.833 s
%------------------------------------------------------------------------------