Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV286-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:58:43 AM UTC 2026

% Result   : Unsatisfiable 76.14s 27.60s
% Output   : Refutation 77.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :  357
% Syntax   : Number of formulae    : 2094 ( 748 unt;   0 typ;  24 def)
%            Number of atoms       : 4988 (2471 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 21799 (2911   ~;1958   |;   0   &;16930   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  156 ( 153 usr;  24 con; 0-6 aty)
%            Number of variables   : 4621 (   0   ^;4573   !;  24   ?;4621   :)
%                                         (   0  !>;   0  ?*;   0  @-;  24  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_decl,type,
    c_in: $i > $i > $i > $o ).

thf(c_Event_Oevent_OSays_decl,type,
    c_Event_Oevent_OSays: $i > $i > $i > $i ).

thf(v_B_H_decl,type,
    v_B_H: $i ).

thf(v_A_decl,type,
    v_A: $i ).

thf(c_Message_Omsg_OMPair_decl,type,
    c_Message_Omsg_OMPair: $i > $i > $i ).

thf(v_NA_decl,type,
    v_NA: $i ).

thf(c_Message_Omsg_OCrypt_decl,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

thf(c_Public_OshrK_decl,type,
    c_Public_OshrK: $i > $i ).

thf(c_Message_Omsg_OKey_decl,type,
    c_Message_Omsg_OKey: $i > $i ).

thf(v_K_decl,type,
    v_K: $i ).

thf(c_List_Oset_decl,type,
    c_List_Oset: $i > $i > $i ).

thf(v_evs_decl,type,
    v_evs: $i ).

thf(tc_Event_Oevent_decl,type,
    tc_Event_Oevent: $i ).

thf(v_B_decl,type,
    v_B: $i ).

thf(c_Message_Omsg_OAgent_decl,type,
    c_Message_Omsg_OAgent: $i > $i ).

thf(c_Event_Obad_decl,type,
    c_Event_Obad: $i ).

thf(tc_Message_Oagent_decl,type,
    tc_Message_Oagent: $i ).

thf(c_OtwayRees_Ootway_decl,type,
    c_OtwayRees_Ootway: $i ).

thf(tc_List_Olist_decl,type,
    tc_List_Olist: $i > $i ).

thf(c_Message_Oagent_OServer_decl,type,
    c_Message_Oagent_OServer: $i ).

thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
    c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).

thf(c_Relation_Oconverse_decl,type,
    c_Relation_Oconverse: $i > $i > $i > $i ).

thf(c_lessequals_decl,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_0_decl,type,
    c_0: $i ).

thf(tc_nat_decl,type,
    tc_nat: $i ).

thf(c_List_Olist_ONil_decl,type,
    c_List_Olist_ONil: $i ).

thf(c_List_Orev_decl,type,
    c_List_Orev: $i > $i > $i ).

thf(c_Pair_decl,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(c_Wellfounded__Relations_Oless__than_decl,type,
    c_Wellfounded__Relations_Oless__than: $i ).

thf(tc_prod_decl,type,
    tc_prod: $i > $i > $i ).

thf(c_less_decl,type,
    c_less: $i > $i > $i > $o ).

thf(c_Message_OHPair_decl,type,
    c_Message_OHPair: $i > $i > $i ).

thf(c_Message_Omsg_ONumber_decl,type,
    c_Message_Omsg_ONumber: $i > $i ).

thf(tc_set_decl,type,
    tc_set: $i > $i ).

thf(c_Datatype__Universe_OIn1_decl,type,
    c_Datatype__Universe_OIn1: $i > $i > $i > $i ).

thf(c_emptyset_decl,type,
    c_emptyset: $i ).

thf(c_Datatype__Universe_OIn0_decl,type,
    c_Datatype__Universe_OIn0: $i > $i > $i > $i ).

thf(c_Message_Omsg_ONonce_decl,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(c_Datatype__Universe_Odprod_decl,type,
    c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).

thf(tc_Datatype__Universe_Onode_decl,type,
    tc_Datatype__Universe_Onode: $i > $i > $i ).

thf(c_Datatype__Universe_OScons_decl,type,
    c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__1_decl,type,
    c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__2_decl,type,
    c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__3_decl,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__4_decl,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olist_OCons_decl,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(c_append_decl,type,
    c_append: $i > $i > $i > $i ).

thf(c_Finite__Set_OFinites_decl,type,
    c_Finite__Set_OFinites: $i ).

thf(c_insert_decl,type,
    c_insert: $i > $i > $i > $i ).

thf(c_SetInterval_OgreaterThanAtMost_decl,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(c_SetInterval_OatLeastAtMost_decl,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(c_Message_Oagent_OFriend_decl,type,
    c_Message_Oagent_OFriend: $i > $i ).

thf(c_Message_Oagent_OSpy_decl,type,
    c_Message_Oagent_OSpy: $i ).

thf(c_Nat_Osize_decl,type,
    c_Nat_Osize: $i > $i > $i ).

thf(c_Wellfounded__Recursion_Owf_decl,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

thf(c_Wellfounded__Relations_Olex__prod_decl,type,
    c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).

thf(c_union_decl,type,
    c_union: $i > $i > $i > $i ).

thf(c_Event_Oevent_OGets_decl,type,
    c_Event_Oevent_OGets: $i > $i > $i ).

thf(c_Message_Osynth_decl,type,
    c_Message_Osynth: $i > $i ).

thf(tc_Message_Omsg_decl,type,
    tc_Message_Omsg: $i ).

thf(c_Message_Omsg_OHash_decl,type,
    c_Message_Omsg_OHash: $i > $i ).

thf(c_Message_Oparts_decl,type,
    c_Message_Oparts: $i > $i ).

thf(c_Message_Oanalz_decl,type,
    c_Message_Oanalz: $i > $i ).

thf(c_SetInterval_OatLeastLessThan_decl,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_Pow_decl,type,
    c_Pow: $i > $i > $i ).

thf(c_Relation_Orel__comp_decl,type,
    c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).

thf(c_Public_OpublicKey_decl,type,
    c_Public_OpublicKey: $i > $i > $i ).

thf(c_SetInterval_OatMost_decl,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(c_UNIV_decl,type,
    c_UNIV: $i ).

thf(c_Message_OinvKey_decl,type,
    c_Message_OinvKey: $i > $i ).

thf(c_Message_OsymKeys_decl,type,
    c_Message_OsymKeys: $i ).

thf(c_minus_decl,type,
    c_minus: $i > $i > $i > $i ).

thf(c_List_Oremdups_decl,type,
    c_List_Oremdups: $i > $i > $i ).

thf(c_Event_Oevent_ONotes_decl,type,
    c_Event_Oevent_ONotes: $i > $i > $i ).

thf(c_Datatype__Universe_Odsum_decl,type,
    c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).

thf(c_Relation_OId_decl,type,
    c_Relation_OId: $i ).

thf(c_Relation_OImage_decl,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(c_Sum__Type_OInr_decl,type,
    c_Sum__Type_OInr: $i > $i > $i > $i ).

thf(c_Sum__Type_OInl_decl,type,
    c_Sum__Type_OInl: $i > $i > $i > $i ).

thf(c_inter_decl,type,
    c_inter: $i > $i > $i > $i ).

thf(c_List_Odistinct_decl,type,
    c_List_Odistinct: $i > $i > $o ).

thf(c_Event_Oknows_decl,type,
    c_Event_Oknows: $i > $i > $i ).

thf(c_Event_Oused_decl,type,
    c_Event_Oused: $i > $i ).

thf(c_Transitive__Closure_Otrancl_decl,type,
    c_Transitive__Closure_Otrancl: $i > $i > $i ).

thf(c_Transitive__Closure_Ortrancl_decl,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(c_Event_OinitState_decl,type,
    c_Event_OinitState: $i > $i ).

thf(c_SetInterval_OlessThan_decl,type,
    c_SetInterval_OlessThan: $i > $i > $i ).

thf(c_Main_OImageE__1_decl,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Sum__Type_OPlus_decl,type,
    c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).

thf(tc_sum_decl,type,
    tc_sum: $i > $i > $i ).

thf(c_Main_OPlusE__1_decl,type,
    c_Main_OPlusE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OPlusE__2_decl,type,
    c_Main_OPlusE__2: $i > $i > $i > $i > $i ).

thf(c_Relation_Odiag_decl,type,
    c_Relation_Odiag: $i > $i > $i ).

thf(c_Datatype__Universe_Ouprod_decl,type,
    c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).

thf(c_SetInterval_OgreaterThanLessThan_decl,type,
    c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).

thf(c_Datatype_Ooption_OSome_decl,type,
    c_Datatype_Ooption_OSome: $i > $i > $i ).

thf(c_Union_decl,type,
    c_Union: $i > $i > $i ).

thf(c_Main_OUnionE__1_decl,type,
    c_Main_OUnionE__1: $i > $i > $i > $i ).

thf(c_Relation_ORange_decl,type,
    c_Relation_ORange: $i > $i > $i > $i ).

thf(c_Main_ORangeE__1_decl,type,
    c_Main_ORangeE__1: $i > $i > $i > $i > $i ).

thf(c_List_Olists_decl,type,
    c_List_Olists: $i > $i > $i ).

thf(c_Main_OsubsetI__1_decl,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_Main_OconverseE__1_decl,type,
    c_Main_OconverseE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OconverseE__2_decl,type,
    c_Main_OconverseE__2: $i > $i > $i > $i > $i ).

thf(c_List_Olistrel_decl,type,
    c_List_Olistrel: $i > $i > $i ).

thf(c_Main_Olistrel__Cons1__1_decl,type,
    c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Oin__listsI__1_decl,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

thf(c_Inter_decl,type,
    c_Inter: $i > $i > $i ).

thf(c_Main_OInterI__1_decl,type,
    c_Main_OInterI__1: $i > $i > $i > $i ).

thf(c_Main_OuprodE__1_decl,type,
    c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OuprodE__2_decl,type,
    c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Datatype_Oo2s_decl,type,
    c_Datatype_Oo2s: $i > $i > $i ).

thf(c_Main_Olistrel__Cons2__1_decl,type,
    c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Olistrel__Cons2__2_decl,type,
    c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).

thf(c_Infinite__Set_Oatmost__one_decl,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(c_Main_Orel__compE__1_decl,type,
    c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_Orel__compE__3_decl,type,
    c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_Ofinite__Union__1_decl,type,
    c_Main_Ofinite__Union__1: $i > $i > $i ).

thf(v_sko__usf_decl,type,
    v_sko__usf: $i > $i > $i > $i ).

thf(v_sko__u8o_decl,type,
    v_sko__u8o: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdiagE__1_decl,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(c_Main_Orel__compE__2_decl,type,
    c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_OIdE__1_decl,type,
    c_Main_OIdE__1: $i > $i > $i ).

thf(c_Main_Olistrel__Cons1__2_decl,type,
    c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olex_decl,type,
    c_List_Olex: $i > $i > $i ).

thf(v_sko__vEb_decl,type,
    v_sko__vEb: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olenlex_decl,type,
    c_List_Olenlex: $i > $i > $i ).

thf(c_Relation_ODomain_decl,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(c_Main_ODomainE__1_decl,type,
    c_Main_ODomainE__1: $i > $i > $i > $i > $i ).

thf(sk1_decl,type,
    sk1: $i > $i > $i > $i ).

thf(sk2_decl,type,
    sk2: $i > $i > $i > $i ).

thf(sk3_decl,type,
    sk3: $i > $i ).

thf(sk4_decl,type,
    sk4: $i > $i ).

thf(sk5_decl,type,
    sk5: $i > $i > $i ).

thf(sk6_decl,type,
    sk6: $i > $i > $i > $i > $i ).

thf(sk7_decl,type,
    sk7: $i > $i > $i ).

thf(sk8_decl,type,
    sk8: $i > $i > $i ).

thf(sk9_decl,type,
    sk9: $i > $i > $i ).

thf(sk10_decl,type,
    sk10: $i > $i > $i > $i ).

thf(sk11_decl,type,
    sk11: $i > $i > $i ).

thf(sk12_decl,type,
    sk12: $i > $i ).

thf(sk15_decl,type,
    sk15: $i > $i > $i ).

thf(sk16_decl,type,
    sk16: $i > $i > $i ).

thf(sk19_decl,type,
    sk19: $i > $i > $i ).

thf(sk22_decl,type,
    sk22: $i > $i > $i ).

thf(sk23_decl,type,
    sk23: $i > $i > $i ).

thf(sk24_decl,type,
    sk24: $i > $i ).

thf(sk28_decl,type,
    sk28: $i > $i > $i ).

thf(sk29_decl,type,
    sk29: $i > $i ).

thf(sk30_decl,type,
    sk30: $i > $i ).

thf(sk31_decl,type,
    sk31: $i > $i > $i ).

thf(sk33_decl,type,
    sk33: $i > $i > $i ).

thf(sk36_decl,type,
    sk36: $i > $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ A ) ) )
          = B ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ A ) ) )
          = B ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Omsg_ONonce @ A )
          = B ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Omsg_ONumber @ A )
          = B ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( @+[A: $i > $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
          = B ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk8_def,definition,
    ( sk8
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Public_OpublicKey ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk9_def,definition,
    ( sk9
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Message_OHPair ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk10_def,definition,
    ( sk10
    = ( @+[A: $i > $i > $i > $i] :
        ! [B: $i,C: $i,D: $i] :
          ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
          = B ) ) ) ).

thf(sk11_def,definition,
    ( sk11
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk12_def,definition,
    ( sk12
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Omsg_OHash @ A )
          = B ) ) ) ).

thf(sk15_def,definition,
    ( sk15
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk16_def,definition,
    ( sk16
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk22_def,definition,
    ( sk22
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk23_def,definition,
    ( sk23
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk24_def,definition,
    ( sk24
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Oagent_OFriend @ A )
          = B ) ) ) ).

thf(sk28_def,definition,
    ( sk28
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk29_def,definition,
    ( sk29
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Omsg_OKey @ A )
          = B ) ) ) ).

thf(sk30_def,definition,
    ( sk30
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Public_OshrK @ A )
          = B ) ) ) ).

thf(sk31_def,definition,
    ( sk31
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk33_def,definition,
    ( sk33
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
          = C ) ) ) ).

thf(sk36_def,definition,
    ( sk36
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Message_Omsg_OAgent @ A )
          = B ) ) ) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(307,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(1102,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(464,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(465,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[464]) ).

thf(22079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,465]) ).

thf(22080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22079]) ).

thf(22081,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22080:[bind(A,$thf( A )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( A )),bind(D,$thf( c_UNIV ))]]) ).

thf(22318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,465]) ).

thf(22319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22318]) ).

thf(22320,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22319:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_UNIV @ c_Message_Oparts ))]]) ).

thf(22948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,465]) ).

thf(22949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22948]) ).

thf(22950,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22949:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ))]]) ).

thf(23419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,465]) ).

thf(23420,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23419]) ).

thf(23421,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[23420:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ))]]) ).

thf(24120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,465]) ).

thf(24121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24120]) ).

thf(24122,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[24121:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ))]]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(1150,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(1151,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[1150]) ).

thf(26070,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,1151]) ).

thf(26071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26070]) ).

thf(26197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[26071]) ).

thf(26250,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[26197]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(400,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(401,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[400]) ).

thf(402,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[401]) ).

thf(247,axiom,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_0) ).

thf(962,plain,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(3,negated_conjecture,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(338,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(341,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[338]) ).

thf(1178,plain,
    ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,341]) ).

thf(1179,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1178]) ).

thf(1184,plain,
    ( ( tc_Message_Oagent != tc_Message_Oagent )
    | ( c_Event_Obad != c_Event_Obad )
    | ( c_Message_Oagent_OSpy != v_A ) ),
    inference(simp,[status(thm)],[1179]) ).

thf(1187,plain,
    c_Message_Oagent_OSpy != v_A,
    inference(simp,[status(thm)],[1184]) ).

thf(1717,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != v_A )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1187]) ).

thf(1718,plain,
    ( ( c_0 != v_A )
    | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1717:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(9,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).

thf(346,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(347,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    inference(lifteq,[status(thm)],[346]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(227,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(909,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).

thf(518,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_0) ).

thf(941,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_0) ).

thf(479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(1105,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(cnf,[status(esa)],[479]) ).

thf(481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(lifteq,[status(thm)],[480]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(351,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(352,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[351]) ).

thf(266,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(1003,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(1004,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(lifteq,[status(thm)],[1003]) ).

thf(1951,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( c_List_Olist_ONil @ c_List_Oset ) ) )
      | ( c_emptyset = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1004]) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( c_emptyset = c_0 )
      | ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1951:[bind(A,$thf( D @ ( c_List_Olist_ONil @ c_List_Oset ) )),bind(B,$thf( D ))]]) ).

thf(2112,plain,
    ! [A: $i] :
      ( ( c_emptyset = c_0 )
      | ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1952]) ).

thf(13195,plain,
    ( ( c_emptyset = c_0 )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(rewrite,[status(thm)],[2112,1004]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

thf(447,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(448,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[447]) ).

thf(449,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[448]) ).

thf(1,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(335,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(1395,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
       != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[335,1151]) ).

thf(1396,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
     != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1395]) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent != B )
      | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
       != c_emptyset )
      | ( ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1396]) ).

thf(1415,plain,
    ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
   != c_emptyset ),
    inference(simp,[status(thm)],[1406]) ).

thf(1444,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
       != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
      | ( c_emptyset != c_emptyset ) ),
    inference(paramod_ordered,[status(thm)],[1004,1415]) ).

thf(1445,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
     != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) ),
    inference(simp,[status(thm)],[1444]) ).

thf(1446,plain,
    ! [A: $i] :
      ( ( A != tc_Event_Oevent )
      | ( c_List_Olist_ONil != v_evs ) ),
    inference(simp,[status(thm)],[1445]) ).

thf(1447,plain,
    c_List_Olist_ONil != v_evs,
    inference(simp,[status(thm)],[1446]) ).

thf(14710,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil != c_List_Olist_ONil )
      | ( A != v_evs )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[449,1447]) ).

thf(14711,plain,
    ! [B: $i,A: $i] :
      ( ( A != v_evs )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[14710:[]]) ).

thf(16089,plain,
    ! [A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(simp,[status(thm)],[14711]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(378,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(379,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[378]) ).

thf(16509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( B @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[16089,379]) ).

thf(16510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( C @ ( B @ c_less ) ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[16509]) ).

thf(16511,plain,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[16510:[bind(A,$thf( F )),bind(B,$thf( c_0 )),bind(C,$thf( F @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ))]]) ).

thf(16613,plain,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
    inference(simp,[status(thm)],[16511]) ).

thf(18098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[16613,1151]) ).

thf(18099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[18098]) ).

thf(18231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
       != C )
      | ( c_emptyset != c_Wellfounded__Relations_Oless__than )
      | ( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
       != B ) ),
    inference(simp,[status(thm)],[18099]) ).

thf(18273,plain,
    c_emptyset != c_Wellfounded__Relations_Oless__than,
    inference(simp,[status(thm)],[18231]) ).

thf(18311,plain,
    ( ( c_emptyset != c_emptyset )
    | ( c_Wellfounded__Relations_Oless__than != c_0 )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13195,18273]) ).

thf(18312,plain,
    ( ( c_Wellfounded__Relations_Oless__than != c_0 )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[18311:[]]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(369,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(370,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[369]) ).

thf(18642,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[18312,370]) ).

thf(18643,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18642]) ).

thf(18689,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != c_emptyset )
      | ( c_0 != A )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18643]) ).

thf(18691,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18689]) ).

thf(8,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(345,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(403,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(404,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[403]) ).

thf(405,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[404]) ).

thf(62,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(490,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(491,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[490]) ).

thf(1316,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,491]) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1316]) ).

thf(1322,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ tc_set ) )
      | ( c_UNIV != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[1317]) ).

thf(1328,plain,
    c_UNIV != c_Finite__Set_OFinites,
    inference(simp,[status(thm)],[1322]) ).

thf(6710,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1328]) ).

thf(6711,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6710:[bind(A,$thf( c_UNIV ))]]) ).

thf(8385,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,6711]) ).

thf(8386,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[8385]) ).

thf(8416,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_UNIV != c_0 )
      | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[8386]) ).

thf(8417,plain,
    ( ( c_UNIV != c_0 )
    | ( c_Finite__Set_OFinites != c_0 ) ),
    inference(simp,[status(thm)],[8416]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_1) ).

thf(523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_1) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[502]) ).

thf(504,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[503]) ).

thf(333,axiom,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK_AX_A_58_AsymKeys_0) ).

thf(1159,plain,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1159,1151]) ).

thf(1392,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1391]) ).

thf(1404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat != C )
      | ( c_Message_OsymKeys != c_emptyset )
      | ( ( A @ c_Public_OshrK )
       != B ) ),
    inference(simp,[status(thm)],[1392]) ).

thf(1413,plain,
    c_Message_OsymKeys != c_emptyset,
    inference(simp,[status(thm)],[1404]) ).

thf(33648,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c_Message_OsymKeys )
      | ( B != c_emptyset )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1413]) ).

thf(33649,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_emptyset )
      | ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33648:[bind(A,$thf( c_Message_OsymKeys ))]]) ).

thf(36162,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ),
    inference(simp,[status(thm)],[33649]) ).

thf(1593,plain,
    ! [A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( c_0 != v_evs )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1447]) ).

thf(1594,plain,
    ( ( c_0 != v_evs )
    | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1593:[bind(A,$thf( c_List_Olist_ONil ))]]) ).

thf(162,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(748,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(749,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[748]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(790,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(791,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(lifteq,[status(thm)],[790]) ).

thf(1453,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(rewrite,[status(thm)],[749,791]) ).

thf(2157,plain,
    ( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ~ $true
    | ( c_0 != v_evs ) ),
    inference(paramod_ordered,[status(thm)],[1594,1453]) ).

thf(2158,plain,
    ( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2157]) ).

thf(2161,plain,
    ( ( tc_nat != tc_nat )
    | ( c_List_Olist_ONil != c_0 )
    | ( c_0 != c_0 )
    | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2158]) ).

thf(2166,plain,
    ( ( c_List_Olist_ONil != c_0 )
    | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2161]) ).

thf(2177,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_List_Olist_ONil != c_0 )
      | ( A != v_evs )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,2166]) ).

thf(2178,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil != c_0 )
      | ( A != v_evs )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2177:[]]) ).

thf(2179,plain,
    ( ( c_List_Olist_ONil != c_0 )
    | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2178]) ).

thf(6693,plain,
    ! [A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,2179]) ).

thf(6694,plain,
    ! [A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6693]) ).

thf(6695,plain,
    ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6694:[bind(A,$thf( c_List_Olist_ONil ))]]) ).

thf(1454,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
      | ~ $true
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[352,1453]) ).

thf(1455,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1454]) ).

thf(1456,plain,
    ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[1455:[bind(A,$thf( c_0 )),bind(B,$thf( c_0 ))]]) ).

thf(1481,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,1456]) ).

thf(1482,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1481]) ).

thf(1488,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ ( tc_nat @ tc_prod ) ) )
      | ( c_UNIV != c_Wellfounded__Relations_Oless__than )
      | ( A
       != ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) ) ) ),
    inference(simp,[status(thm)],[1482]) ).

thf(1496,plain,
    c_UNIV != c_Wellfounded__Relations_Oless__than,
    inference(simp,[status(thm)],[1488]) ).

thf(33596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c_UNIV )
      | ( B != c_Wellfounded__Relations_Oless__than )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1496]) ).

thf(33597,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33596:[bind(A,$thf( c_UNIV ))]]) ).

thf(36138,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ),
    inference(simp,[status(thm)],[33597]) ).

thf(42698,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36138]) ).

thf(42699,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42698]) ).

thf(42880,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42699]) ).

thf(42927,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42880]) ).

thf(218,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).

thf(886,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(22144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[886,465]) ).

thf(22145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22144]) ).

thf(22146,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22145:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ c_Message_Omsg_OAgent )),bind(D,$thf( F @ c_Message_Osynth ))]]) ).

thf(22193,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    inference(simp,[status(thm)],[22146]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK__D__dest_0) ).

thf(1073,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(33598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != c_UNIV )
      | ( A != c_Wellfounded__Relations_Oless__than )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1496]) ).

thf(33599,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ~ ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33598:[bind(A,$thf( A )),bind(B,$thf( c_UNIV ))]]) ).

thf(36139,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ),
    inference(simp,[status(thm)],[33599]) ).

thf(45287,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36139]) ).

thf(45288,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45287]) ).

thf(45321,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45288]) ).

thf(45366,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45321]) ).

thf(41,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(436,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(437,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(cnf,[status(esa)],[436]) ).

thf(438,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[437]) ).

thf(439,plain,
    ? [A: $i > $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[438]) ).

thf(440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk6 ) ) ) )
      = A ),
    inference(cnf,[status(esa)],[439]) ).

thf(13424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk6 ) ) ) )
      = A ),
    inference(lifteq,[status(thm)],[440]) ).

thf(71,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

thf(511,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(5,negated_conjecture,
    tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(334,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
       != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,1151]) ).

thf(1388,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
     != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1387]) ).

thf(1405,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist )
       != B )
      | ( c_emptyset != c_OtwayRees_Ootway )
      | ( v_evs != A ) ),
    inference(simp,[status(thm)],[1388]) ).

thf(1414,plain,
    c_emptyset != c_OtwayRees_Ootway,
    inference(simp,[status(thm)],[1405]) ).

thf(1658,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_0 != c_OtwayRees_Ootway )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1414]) ).

thf(1659,plain,
    ( ( c_0 != c_OtwayRees_Ootway )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1658:[bind(A,$thf( c_emptyset ))]]) ).

thf(6740,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1659]) ).

thf(6741,plain,
    ! [A: $i] :
      ( ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6740:[]]) ).

thf(7516,plain,
    ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6741]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).

thf(952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(953,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(cnf,[status(esa)],[952]) ).

thf(954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(lifteq,[status(thm)],[953]) ).

thf(955,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[954]) ).

thf(956,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk31 ) )
      = B ),
    inference(cnf,[status(esa)],[955]) ).

thf(18951,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk31 ) )
      = B ),
    inference(lifteq,[status(thm)],[956]) ).

thf(22288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,1151]) ).

thf(22289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22288]) ).

thf(22357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[22289]) ).

thf(22383,plain,
    ( ( c_UNIV @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[22357]) ).

thf(22423,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( ( c_0 @ c_Message_Oparts )
       != c_emptyset )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,22383]) ).

thf(22424,plain,
    ( ( ( c_0 @ c_Message_Oparts )
     != c_emptyset )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[22423:[bind(A,$thf( c_UNIV ))]]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(406,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    inference(polarity_switch,[status(thm)],[406]) ).

thf(408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    inference(lifteq,[status(thm)],[407]) ).

thf(165,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(757,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(57,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).

thf(475,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(476,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[475]) ).

thf(14158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,476]) ).

thf(14159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14158]) ).

thf(14205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != tc_Message_Omsg )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[14159]) ).

thf(14235,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[14205]) ).

thf(46794,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36162]) ).

thf(46795,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46794]) ).

thf(46900,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46795]) ).

thf(46976,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46900]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_1) ).

thf(681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(cnf,[status(esa)],[681]) ).

thf(683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(lifteq,[status(thm)],[682]) ).

thf(684,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[683]) ).

thf(685,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk19 ) )
      = B ),
    inference(cnf,[status(esa)],[684]) ).

thf(13548,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk19 ) )
      = B ),
    inference(lifteq,[status(thm)],[685]) ).

thf(113,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(616,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(617,plain,
    c_UNIV != c_emptyset,
    inference(polarity_switch,[status(thm)],[616]) ).

thf(618,plain,
    c_UNIV != c_emptyset,
    inference(lifteq,[status(thm)],[617]) ).

thf(6795,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,618]) ).

thf(6796,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6795:[bind(A,$thf( c_UNIV ))]]) ).

thf(63,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(492,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1575,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,492]) ).

thf(1576,plain,
    ( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
    | ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1575:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(2247,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1576]) ).

thf(2248,plain,
    ( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
    | ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2247:[bind(A,$thf( tc_nat ))]]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).

thf(1041,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
      = ( B @ ( A @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff2_0) ).

thf(861,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
      = ( B @ ( A @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(1078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(23,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(385,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(38951,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( ( c_0 @ c_Message_Oparts )
       != c_emptyset )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,22424]) ).

thf(38952,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( ( c_0 @ c_Message_Oparts )
       != c_emptyset ) ),
    inference(simp,[status(thm)],[38951]) ).

thf(38997,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_UNIV != c_0 )
      | ( ( c_0 @ c_Message_Oparts )
       != c_emptyset ) ),
    inference(simp,[status(thm)],[38952]) ).

thf(39011,plain,
    ( ( c_UNIV != c_0 )
    | ( ( c_0 @ c_Message_Oparts )
     != c_emptyset ) ),
    inference(simp,[status(thm)],[38997]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(250,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(967,plain,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(8503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[967,1151]) ).

thf(8504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[8503]) ).

thf(8545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist )
       != D )
      | ( ( B @ ( A @ c_List_Olists ) )
       != c_emptyset )
      | ( c_List_Olist_ONil != C ) ),
    inference(simp,[status(thm)],[8504]) ).

thf(8568,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Olists ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[8545]) ).

thf(4,negated_conjecture,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(339,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(340,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[339]) ).

thf(1160,plain,
    ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,340]) ).

thf(1161,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1160]) ).

thf(1164,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Oagent )
    | ( c_OtwayRees_Ootway != c_Event_Obad )
    | ( v_B != v_evs ) ),
    inference(simp,[status(thm)],[1161]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).

thf(471,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(472,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[471]) ).

thf(2155,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_evs ) ),
    inference(paramod_ordered,[status(thm)],[1594,370]) ).

thf(2156,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2155]) ).

thf(2163,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != c_List_Olist_ONil )
      | ( c_0 != A )
      | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2156]) ).

thf(2168,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_emptyset != c_List_Olist_ONil )
      | ( c_0 != v_evs ) ),
    inference(simp,[status(thm)],[2163]) ).

thf(6550,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1415]) ).

thf(6551,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6550:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).

thf(42770,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36138]) ).

thf(42771,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42770]) ).

thf(42908,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42771]) ).

thf(42959,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42908]) ).

thf(81,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(538,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(46812,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36162]) ).

thf(46813,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46812]) ).

thf(46938,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46813]) ).

thf(47018,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46938]) ).

thf(210,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).

thf(866,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(867,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(polarity_switch,[status(thm)],[866]) ).

thf(868,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(lifteq,[status(thm)],[867]) ).

thf(33594,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != c_Message_Oagent_OSpy )
      | ( A != c_Message_Oagent_OServer )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,868]) ).

thf(33595,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_Message_Oagent_OServer )
      | ~ ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33594:[bind(A,$thf( A )),bind(B,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(36137,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(simp,[status(thm)],[33595]) ).

thf(6,negated_conjecture,
    ! [B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(336,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(342,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[336]) ).

thf(1308,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,342]) ).

thf(1309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1308]) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_Event_Oevent )
      | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
       != c_UNIV )
      | ( A
       != ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(simp,[status(thm)],[1309]) ).

thf(1329,plain,
    ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
   != c_UNIV ),
    inference(simp,[status(thm)],[1323]) ).

thf(6726,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1329]) ).

thf(6727,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6726:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).

thf(2283,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(paramod_ordered,[status(thm)],[1659,370]) ).

thf(2284,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2283]) ).

thf(2291,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != c_emptyset )
      | ( c_0 != A )
      | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2284]) ).

thf(2296,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2291]) ).

thf(6616,plain,
    ! [B: $i,A: $i] :
      ( ( c_0 != c_0 )
      | ( ( B @ tc_set )
       != tc_nat )
      | ( A != c_OtwayRees_Ootway )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,2296]) ).

thf(6617,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( A != c_OtwayRees_Ootway )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6616:[]]) ).

thf(7484,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6617]) ).

thf(1306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,476]) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1306]) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_UNIV )
      | ( A != C ) ),
    inference(simp,[status(thm)],[1307]) ).

thf(1327,plain,
    ( ( c_emptyset @ c_Message_Oparts )
   != c_UNIV ),
    inference(simp,[status(thm)],[1321]) ).

thf(26113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,465]) ).

thf(26114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26113]) ).

thf(26115,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[26114:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ))]]) ).

thf(40952,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36137]) ).

thf(40953,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40952]) ).

thf(41024,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40953]) ).

thf(41101,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41024]) ).

thf(2281,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1659]) ).

thf(2282,plain,
    ! [A: $i] :
      ( ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2281:[]]) ).

thf(2299,plain,
    ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2282]) ).

thf(5177,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,2299]) ).

thf(5178,plain,
    ( ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5177:[bind(A,$thf( tc_nat ))]]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4__iff1_0) ).

thf(1063,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(1190,plain,
    ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,491]) ).

thf(1191,plain,
    ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1190]) ).

thf(1196,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_Message_Oagent )
    | ( c_Finite__Set_OFinites != c_Event_Obad )
    | ( c_UNIV != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[1191]) ).

thf(22294,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,476]) ).

thf(22295,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22294]) ).

thf(22353,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[22295]) ).

thf(22379,plain,
    ( ( c_UNIV @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[22353]) ).

thf(265,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(1001,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(46792,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36162]) ).

thf(46793,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46792]) ).

thf(46890,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46793]) ).

thf(46966,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46890]) ).

thf(122,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(640,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(1431,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[640,491]) ).

thf(1432,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1431]) ).

thf(1440,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[1432]) ).

thf(1441,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[1440]) ).

thf(42792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36138]) ).

thf(42793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42792]) ).

thf(42917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42793]) ).

thf(42968,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[42917]) ).

thf(42790,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36138]) ).

thf(42791,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42790]) ).

thf(42868,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42791]) ).

thf(43004,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42868]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState__iff1_0) ).

thf(622,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(623,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[622]) ).

thf(21991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[465,623]) ).

thf(21992,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[21991]) ).

thf(21993,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[21992:[bind(A,$thf( E @ c_Message_Omsg_ONonce )),bind(B,$thf( F @ c_Event_OinitState )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).

thf(22261,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(simp,[status(thm)],[21993]) ).

thf(28724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,22261]) ).

thf(28725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[28724]) ).

thf(28863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[28725]) ).

thf(28907,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[28863]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).

thf(829,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(304,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(1095,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(709,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(13250,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_emptyset = c_0 )
      | ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,13195]) ).

thf(13251,plain,
    ( ( c_emptyset = c_0 )
    | ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[13250:[bind(A,$thf( tc_nat ))]]) ).

thf(18320,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_Wellfounded__Relations_Oless__than != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,18273]) ).

thf(18321,plain,
    ( ( c_Wellfounded__Relations_Oless__than != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[18320:[bind(A,$thf( c_emptyset ))]]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0) ).

thf(883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    inference(polarity_switch,[status(thm)],[883]) ).

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    inference(lifteq,[status(thm)],[884]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(1046,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(1644,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
      | ( c_UNIV != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1329]) ).

thf(1645,plain,
    ( ( c_UNIV != c_0 )
    | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1644:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).

thf(33592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( B != c_Message_Oagent_OServer )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,868]) ).

thf(33593,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_Message_Oagent_OServer )
      | ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33592:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(36136,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ),
    inference(simp,[status(thm)],[33593]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).

thf(409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(cnf,[status(esa)],[409]) ).

thf(411,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(lifteq,[status(thm)],[410]) ).

thf(412,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[411]) ).

thf(413,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Orev ) @ ( B @ sk5 ) )
      = A ),
    inference(cnf,[status(esa)],[412]) ).

thf(8671,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Orev ) @ ( B @ sk5 ) )
      = A ),
    inference(lifteq,[status(thm)],[413]) ).

thf(22014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,465]) ).

thf(22015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22014]) ).

thf(22016,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22015:[bind(A,$thf( E )),bind(B,$thf( tc_Message_Omsg )),bind(C,$thf( E )),bind(D,$thf( tc_Message_Omsg @ ( c_emptyset @ ( E @ c_insert ) ) ))]]) ).

thf(22192,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(simp,[status(thm)],[22016]) ).

thf(33650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != c_Message_OsymKeys )
      | ( A != c_emptyset )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1413]) ).

thf(33651,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_emptyset )
      | ~ ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[33650:[bind(A,$thf( A )),bind(B,$thf( c_Message_OsymKeys ))]]) ).

thf(36163,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
    inference(simp,[status(thm)],[33651]) ).

thf(49567,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36163]) ).

thf(49568,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49567]) ).

thf(49649,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49568]) ).

thf(49764,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49649]) ).

thf(1180,plain,
    ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,340]) ).

thf(1181,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1180]) ).

thf(1185,plain,
    ( ( tc_Message_Oagent != tc_Message_Oagent )
    | ( c_Event_Obad != c_Event_Obad )
    | ( c_Message_Oagent_OSpy != v_B ) ),
    inference(simp,[status(thm)],[1181]) ).

thf(1188,plain,
    c_Message_Oagent_OSpy != v_B,
    inference(simp,[status(thm)],[1185]) ).

thf(34222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( B != v_B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1188]) ).

thf(34223,plain,
    ! [B: $i,A: $i] :
      ( ( A != v_B )
      | ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[34222:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(36442,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ),
    inference(simp,[status(thm)],[34223]) ).

thf(51713,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36442]) ).

thf(51714,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51713]) ).

thf(51827,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51714]) ).

thf(51914,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51827]) ).

thf(201,axiom,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0) ).

thf(850,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(851,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[850]) ).

thf(1290,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1159,851]) ).

thf(1291,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1290]) ).

thf(1298,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_Message_Oagent )
      | ( c_Message_OsymKeys != c_Event_Obad )
      | ( ( A @ c_Public_OshrK )
       != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[1291]) ).

thf(149,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(719,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(371,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(372,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(cnf,[status(esa)],[371]) ).

thf(24079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,623]) ).

thf(24080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24079]) ).

thf(24189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[24080]) ).

thf(24240,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[24189]) ).

thf(24971,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[24240]) ).

thf(1882,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != v_B )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1188]) ).

thf(1883,plain,
    ( ( c_0 != v_B )
    | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1882:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(5013,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_B )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1883]) ).

thf(5014,plain,
    ! [A: $i] :
      ( ( A != v_B )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5013:[]]) ).

thf(5052,plain,
    ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5014]) ).

thf(6065,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,5052]) ).

thf(6066,plain,
    ( ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[6065:[bind(A,$thf( tc_nat ))]]) ).

thf(114,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).

thf(619,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(150,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(721,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1272,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,341]) ).

thf(1273,plain,
    ! [A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1272]) ).

thf(1279,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_Message_Oagent )
      | ( c_Finite__Set_OFinites != c_Event_Obad )
      | ( c_emptyset != v_A ) ),
    inference(simp,[status(thm)],[1273]) ).

thf(49439,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
       != ( A @ ( A @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,36163]) ).

thf(49440,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( A @ ( A @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49439]) ).

thf(49675,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent != A )
      | ( ( A @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != c_Event_Obad )
      | ( c_Message_Oagent_OSpy != c_emptyset ) ),
    inference(simp,[status(thm)],[49440]) ).

thf(49704,plain,
    ( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
     != c_Event_Obad )
    | ( c_Message_Oagent_OSpy != c_emptyset ) ),
    inference(simp,[status(thm)],[49675]) ).

thf(14195,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,491]) ).

thf(14196,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14195]) ).

thf(14198,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ tc_set ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[14196]) ).

thf(14228,plain,
    ( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != c_Finite__Set_OFinites ),
    inference(simp,[status(thm)],[14198]) ).

thf(2285,plain,
    ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ~ $true
    | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(paramod_ordered,[status(thm)],[1659,1453]) ).

thf(2286,plain,
    ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2285]) ).

thf(2289,plain,
    ( ( tc_nat != tc_nat )
    | ( c_emptyset != c_0 )
    | ( c_0 != c_0 )
    | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2286]) ).

thf(2294,plain,
    ( ( c_emptyset != c_0 )
    | ( c_0 != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[2289]) ).

thf(7225,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_emptyset != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,2294]) ).

thf(7226,plain,
    ! [A: $i] :
      ( ( c_emptyset != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7225:[]]) ).

thf(7386,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7226]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).

thf(387,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(388,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    inference(cnf,[status(esa)],[387]) ).

thf(389,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    inference(lifteq,[status(thm)],[388]) ).

thf(60,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(484,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,1151]) ).

thf(1390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1389]) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != C )
      | ( c_Finite__Set_OFinites != c_emptyset )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != B ) ),
    inference(simp,[status(thm)],[1390]) ).

thf(1409,plain,
    c_Finite__Set_OFinites != c_emptyset,
    inference(simp,[status(thm)],[1408]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(38602,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36136]) ).

thf(38603,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38602]) ).

thf(38694,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38603]) ).

thf(38759,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38694]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(785,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(182,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(802,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(343,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(344,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(cnf,[status(esa)],[343]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0) ).

thf(934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).

thf(528,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(529,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    inference(cnf,[status(esa)],[528]) ).

thf(530,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    inference(lifteq,[status(thm)],[529]) ).

thf(531,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Omsg_OHash @ A )
      = B ),
    inference(detectInverse,[status(thm)],[530]) ).

thf(532,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OHash @ sk12 )
      = A ),
    inference(cnf,[status(esa)],[531]) ).

thf(1462,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OHash @ sk12 )
      = A ),
    inference(lifteq,[status(thm)],[532]) ).

thf(286,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

thf(1059,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[540]) ).

thf(542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[541]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).

thf(459,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(460,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[459]) ).

thf(189,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_0) ).

thf(817,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(203,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

thf(853,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(6459,plain,
    ! [A: $i] :
      ( ( A
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1327]) ).

thf(6460,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6459:[bind(A,$thf( c_emptyset @ c_Message_Oparts ))]]) ).

thf(26376,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) )
      | ( c_UNIV != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,6460]) ).

thf(26377,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[26376]) ).

thf(26418,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_0 )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[26377]) ).

thf(26435,plain,
    ( ( ( c_emptyset @ c_Message_Oparts )
     != c_0 )
    | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[26418]) ).

thf(26472,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,26435]) ).

thf(26473,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[26472]) ).

thf(26474,plain,
    ( ( ( c_emptyset @ c_Message_Oparts )
     != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[26473:[bind(A,$thf( c_UNIV ))]]) ).

thf(1513,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,962]) ).

thf(1514,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
    | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1513:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
      | ( c_emptyset != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1415]) ).

thf(1572,plain,
    ( ( c_emptyset != c_0 )
    | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).

thf(22346,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,491]) ).

thf(22347,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22346]) ).

thf(22348,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[22347]) ).

thf(22374,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_Message_Omsg )
    | ( ( c_UNIV @ c_Message_Oparts )
     != c_Finite__Set_OFinites ) ),
    inference(simp,[status(thm)],[22348]) ).

thf(22983,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,491]) ).

thf(22984,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22983]) ).

thf(22999,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
       != c_Finite__Set_OFinites )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[22984]) ).

thf(23026,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_Message_Omsg )
    | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
     != c_Finite__Set_OFinites ) ),
    inference(simp,[status(thm)],[22999]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(373,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    inference(cnf,[status(esa)],[373]) ).

thf(375,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    inference(lifteq,[status(thm)],[374]) ).

thf(376,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ A ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[375]) ).

thf(377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
      = A ),
    inference(cnf,[status(esa)],[376]) ).

thf(5076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[377]) ).

thf(328,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

thf(1147,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(26,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(395,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(396,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[395]) ).

thf(4999,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_B ) ),
    inference(paramod_ordered,[status(thm)],[1883,396]) ).

thf(5000,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[4999]) ).

thf(5037,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( c_0 != A )
      | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[5000]) ).

thf(5047,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[5037]) ).

thf(5061,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_B )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,5047]) ).

thf(5062,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_B )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5061:[]]) ).

thf(5071,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5062]) ).

thf(6362,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[5071,370]) ).

thf(6363,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[6362]) ).

thf(6385,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_B )
      | ( c_0 != A )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[6363]) ).

thf(6396,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_B )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[6385]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2__iff1_0) ).

thf(419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(420,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[419]) ).

thf(421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[420]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).

thf(870,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(16512,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[16089,396]) ).

thf(16513,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) ),
    inference(simp,[status(thm)],[16512]) ).

thf(16576,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )
       != c_0 )
      | ( c_0 != B ) ),
    inference(simp,[status(thm)],[16513]) ).

thf(16584,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )
     != c_0 ),
    inference(simp,[status(thm)],[16576]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).

thf(979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(cnf,[status(esa)],[979]) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(lifteq,[status(thm)],[980]) ).

thf(982,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[981]) ).

thf(983,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk33 ) )
      = B ),
    inference(cnf,[status(esa)],[982]) ).

thf(18988,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk33 ) )
      = B ),
    inference(lifteq,[status(thm)],[983]) ).

thf(49555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36163]) ).

thf(49556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49555]) ).

thf(49662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49556]) ).

thf(49781,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[49662]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(770,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).

thf(881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0) ).

thf(416,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

thf(1115,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(112,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).

thf(615,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(2195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[615,476]) ).

thf(2196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2195]) ).

thf(2215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( B @ c_Message_Osynth )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Message_Omsg_ONumber )
       != C ) ),
    inference(simp,[status(thm)],[2196]) ).

thf(2222,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[2215]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(473,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(474,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[473]) ).

thf(24592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[640,474]) ).

thf(24593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24592]) ).

thf(24594,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[24593:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ c_SetInterval_OlessThan ) )),bind(C,$thf( tc_nat ))]]) ).

thf(24734,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) ),
    inference(simp,[status(thm)],[24594]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(442,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[442]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(1109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(10191,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( E @ ( c_emptyset @ ( D @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[852,1151]) ).

thf(10192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( E @ ( c_emptyset @ ( D @ c_in ) ) ) ),
    inference(simp,[status(thm)],[10191]) ).

thf(10256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != E )
      | ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
       != c_emptyset )
      | ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
       != D ) ),
    inference(simp,[status(thm)],[10192]) ).

thf(10271,plain,
    ! [A: $i] :
      ( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[10256]) ).

thf(4764,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_A )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1718]) ).

thf(4765,plain,
    ! [A: $i] :
      ( ( A != v_A )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4764:[]]) ).

thf(4806,plain,
    ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[4765]) ).

thf(5803,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,4806]) ).

thf(5804,plain,
    ( ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5803:[bind(A,$thf( tc_nat ))]]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey__iff1_0) ).

thf(512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(polarity_switch,[status(thm)],[512]) ).

thf(514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(lifteq,[status(thm)],[513]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(12,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(353,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(233,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(924,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(34224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != c_Message_Oagent_OSpy )
      | ( A != v_B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[504,1188]) ).

thf(34225,plain,
    ! [B: $i,A: $i] :
      ( ( A != v_B )
      | ~ ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(pattern_uni,[status(thm)],[34224:[bind(A,$thf( A )),bind(B,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(36443,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( v_B @ c_in ) ) ),
    inference(simp,[status(thm)],[34225]) ).

thf(53993,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( v_B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36443]) ).

thf(53994,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[53993]) ).

thf(54115,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) ) )
      | ( A != v_B ) ),
    inference(simp,[status(thm)],[53994]) ).

thf(54196,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[54115]) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1159,476]) ).

thf(1285,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1284]) ).

thf(1300,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_nat )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Message_OsymKeys )
      | ( ( A @ c_Public_OshrK )
       != B ) ),
    inference(simp,[status(thm)],[1285]) ).

thf(1302,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[1300]) ).

thf(42772,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36138]) ).

thf(42773,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42772]) ).

thf(42894,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42773]) ).

thf(42944,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42894]) ).

thf(19235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[615,460]) ).

thf(19236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19235]) ).

thf(19237,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19236:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ c_Message_Omsg_ONumber )),bind(D,$thf( B ))]]) ).

thf(19416,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19237]) ).

thf(19610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19416,460]) ).

thf(19611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19610]) ).

thf(19612,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19611:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(19717,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19612]) ).

thf(19892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19717,460]) ).

thf(19893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19892]) ).

thf(19894,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19893:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(20021,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19894]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_0) ).

thf(485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(937,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(94,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(574,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).

thf(1020,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).

thf(348,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(35,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(422,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(423,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[422]) ).

thf(1366,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
      | ~ $true
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[352,423]) ).

thf(1367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1366]) ).

thf(1368,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[1367:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(1384,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(simp,[status(thm)],[1368]) ).

thf(14193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,1384]) ).

thf(14194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14193]) ).

thf(14202,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ ( tc_nat @ tc_prod ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Wellfounded__Relations_Oless__than )
      | ( A
       != ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) ) ) ),
    inference(simp,[status(thm)],[14194]) ).

thf(14232,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
     != c_Wellfounded__Relations_Oless__than ),
    inference(simp,[status(thm)],[14202]) ).

thf(1264,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,476]) ).

thf(1265,plain,
    ! [B: $i,A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1264]) ).

thf(1278,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Finite__Set_OFinites )
      | ( c_emptyset != B ) ),
    inference(simp,[status(thm)],[1265]) ).

thf(1283,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Finite__Set_OFinites ) ),
    inference(simp,[status(thm)],[1278]) ).

thf(283,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(1051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(45230,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36139]) ).

thf(45231,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45230]) ).

thf(45324,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45231]) ).

thf(45369,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45324]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3__iff1_0) ).

thf(397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(877,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[452]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(18637,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,18312]) ).

thf(18638,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[18637]) ).

thf(18639,plain,
    ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[18638:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(4750,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_A ) ),
    inference(paramod_ordered,[status(thm)],[1718,396]) ).

thf(4751,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4750]) ).

thf(4788,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( c_0 != A )
      | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4751]) ).

thf(4801,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4788]) ).

thf(4812,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_A )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,4801]) ).

thf(4813,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_A )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4812:[]]) ).

thf(4825,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[4813]) ).

thf(45238,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36139]) ).

thf(45239,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45238]) ).

thf(45293,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45239]) ).

thf(45423,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45293]) ).

thf(4552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,623]) ).

thf(4553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4552]) ).

thf(4577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_Message_Omsg )
      | ( ( D @ c_Event_OinitState @ c_Message_Oparts )
       != c_UNIV )
      | ( A
       != ( C @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[4553]) ).

thf(4588,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != c_UNIV ),
    inference(simp,[status(thm)],[4577]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(507,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[433]) ).

thf(11935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,434]) ).

thf(11936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[11935]) ).

thf(11937,plain,
    ! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[11936:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).

thf(12090,plain,
    ! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
    inference(simp,[status(thm)],[11937]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,341]) ).

thf(1315,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1314]) ).

thf(1318,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_Message_Oagent )
      | ( c_UNIV != c_Event_Obad )
      | ( A != v_A ) ),
    inference(simp,[status(thm)],[1315]) ).

thf(1324,plain,
    c_UNIV != c_Event_Obad,
    inference(simp,[status(thm)],[1318]) ).

thf(6754,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1324]) ).

thf(6755,plain,
    ( ( c_0 != c_Event_Obad )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6754:[bind(A,$thf( c_UNIV ))]]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(49577,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36163]) ).

thf(49578,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49577]) ).

thf(49656,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49578]) ).

thf(49774,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49656]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(cnf,[status(esa)],[752]) ).

thf(754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(lifteq,[status(thm)],[753]) ).

thf(755,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[754]) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk23 ) )
      = A ),
    inference(cnf,[status(esa)],[755]) ).

thf(14113,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk23 ) )
      = A ),
    inference(lifteq,[status(thm)],[756]) ).

thf(38584,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36136]) ).

thf(38585,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38584]) ).

thf(38679,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38585]) ).

thf(38744,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38679]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(988,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(291,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).

thf(1070,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(9477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1070,476]) ).

thf(9478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[9477]) ).

thf(9533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( B @ ( A @ c_Event_Oknows ) )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != C ) ),
    inference(simp,[status(thm)],[9478]) ).

thf(9556,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oknows ) )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[9533]) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
       != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,1151]) ).

thf(1386,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1385]) ).

thf(1401,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Oagent != B )
      | ( c_emptyset != c_Event_Obad )
      | ( c_Message_Oagent_OSpy != A ) ),
    inference(simp,[status(thm)],[1386]) ).

thf(1410,plain,
    c_emptyset != c_Event_Obad,
    inference(simp,[status(thm)],[1401]) ).

thf(7268,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_0 != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1410]) ).

thf(7269,plain,
    ( ( c_0 != c_Event_Obad )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7268:[bind(A,$thf( c_emptyset ))]]) ).

thf(13623,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
      | ( c_0 != c_Event_Obad )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7269]) ).

thf(13624,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
      | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[13623]) ).

thf(13660,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_emptyset != c_0 )
      | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[13624]) ).

thf(13671,plain,
    ( ( c_emptyset != c_0 )
    | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[13660]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).

thf(380,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(130,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(661,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1660,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_Event_Obad )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1324]) ).

thf(1661,plain,
    ( ( c_0 != c_Event_Obad )
    | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1660:[bind(A,$thf( c_UNIV ))]]) ).

thf(4451,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_Event_Obad )
      | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1661]) ).

thf(4452,plain,
    ! [A: $i] :
      ( ( A != c_Event_Obad )
      | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4451:[]]) ).

thf(4480,plain,
    ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[4452]) ).

thf(7036,plain,
    ! [A: $i] :
      ( ( A != c_Message_OsymKeys )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1413]) ).

thf(7037,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7036:[bind(A,$thf( c_Message_OsymKeys ))]]) ).

thf(29428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,1151]) ).

thf(29429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[29428]) ).

thf(29536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[29429]) ).

thf(29586,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
     != c_emptyset ),
    inference(simp,[status(thm)],[29536]) ).

thf(185,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).

thf(808,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(809,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(polarity_switch,[status(thm)],[808]) ).

thf(810,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(lifteq,[status(thm)],[809]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK__iff1_0) ).

thf(1067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(4439,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != c_Event_Obad ) ),
    inference(paramod_ordered,[status(thm)],[1661,423]) ).

thf(4440,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[4439]) ).

thf(4475,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( c_UNIV != A )
      | ( c_0 != A )
      | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[4440]) ).

thf(4489,plain,
    ( ( c_UNIV != c_0 )
    | ( c_0 != c_Event_Obad ) ),
    inference(simp,[status(thm)],[4475]) ).

thf(6810,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,4489]) ).

thf(6811,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6810:[]]) ).

thf(7533,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6811]) ).

thf(42680,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,36138]) ).

thf(42681,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42680]) ).

thf(42916,plain,
    ! [A: $i] :
      ( ( A != tc_Message_Oagent )
      | ( ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != c_Event_Obad )
      | ( c_UNIV != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[42681]) ).

thf(42967,plain,
    ( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
     != c_Event_Obad )
    | ( c_UNIV != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[42916]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(546,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(40837,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36137]) ).

thf(40838,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40837]) ).

thf(41036,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40838]) ).

thf(41116,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41036]) ).

thf(6461,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( ( c_0 @ c_Message_Oparts )
       != c_UNIV )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1327]) ).

thf(6462,plain,
    ( ( ( c_0 @ c_Message_Oparts )
     != c_UNIV )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6461:[bind(A,$thf( c_emptyset ))]]) ).

thf(26935,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
      | ( ( c_0 @ c_Message_Oparts )
       != c_UNIV )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,6462]) ).

thf(26936,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
      | ( ( c_0 @ c_Message_Oparts )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[26935]) ).

thf(26979,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_emptyset != c_0 )
      | ( ( c_0 @ c_Message_Oparts )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[26936]) ).

thf(26993,plain,
    ( ( c_emptyset != c_0 )
    | ( ( c_0 @ c_Message_Oparts )
     != c_UNIV ) ),
    inference(simp,[status(thm)],[26979]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(366,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(2305,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_emptyset != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,2294]) ).

thf(2306,plain,
    ! [A: $i] :
      ( ( c_emptyset != c_0 )
      | ( A != c_OtwayRees_Ootway )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2305:[]]) ).

thf(2307,plain,
    ( ( c_emptyset != c_0 )
    | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2306]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6__iff1_0) ).

thf(796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    inference(polarity_switch,[status(thm)],[796]) ).

thf(798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    inference(lifteq,[status(thm)],[797]) ).

thf(49515,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,36163]) ).

thf(49516,plain,
    ! [B: $i,A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49515]) ).

thf(49683,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_set )
       != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != c_Finite__Set_OFinites )
      | ( c_emptyset != c_emptyset ) ),
    inference(simp,[status(thm)],[49516]) ).

thf(49712,plain,
    ! [A: $i] :
      ( ( A @ tc_set @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
     != c_Finite__Set_OFinites ),
    inference(simp,[status(thm)],[49683]) ).

thf(228,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(910,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).

thf(1091,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
      | ~ $true
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[352,396]) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1353]) ).

thf(1355,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[1354:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).

thf(1243,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,476]) ).

thf(1244,plain,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1243]) ).

thf(1251,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_OtwayRees_Ootway )
      | ( v_evs != A ) ),
    inference(simp,[status(thm)],[1244]) ).

thf(1255,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Omsg )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_OtwayRees_Ootway ) ),
    inference(simp,[status(thm)],[1251]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_1) ).

thf(598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(42,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(441,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(7816,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[441,491]) ).

thf(7817,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[7816]) ).

thf(7820,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[7817]) ).

thf(7834,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[7820]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).

thf(392,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(18627,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[18312,396]) ).

thf(18628,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18627]) ).

thf(18688,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( c_emptyset != c_0 )
      | ( c_0 != A )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18628]) ).

thf(18690,plain,
    ( ( c_emptyset != c_0 )
    | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[18688]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(424,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(23382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,1151]) ).

thf(23383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23382]) ).

thf(23469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[23383]) ).

thf(23514,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[23469]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(427,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    inference(polarity_switch,[status(thm)],[427]) ).

thf(429,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    inference(lifteq,[status(thm)],[428]) ).

thf(7022,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != c_Message_Oagent_OServer )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,868]) ).

thf(7023,plain,
    ( ( c_0 != c_Message_Oagent_OServer )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7022:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(10355,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) )
      | ( c_0 != c_Message_Oagent_OServer )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7023]) ).

thf(10356,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) )
      | ( c_0 != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[10355]) ).

thf(10386,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( c_0 != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[10356]) ).

thf(10394,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ( c_0 != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[10386]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).

thf(815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(22421,plain,
    ! [A: $i] :
      ( ( A
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,22383]) ).

thf(22422,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[22421:[bind(A,$thf( c_UNIV @ c_Message_Oparts ))]]) ).

thf(30219,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_Message_Oparts @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,22422]) ).

thf(30220,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_Message_Oparts @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[30219]) ).

thf(30262,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_0 )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[30220]) ).

thf(30279,plain,
    ( ( ( c_UNIV @ c_Message_Oparts )
     != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[30262]) ).

thf(30317,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,30279]) ).

thf(30318,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[30317]) ).

thf(30319,plain,
    ( ( ( c_UNIV @ c_Message_Oparts )
     != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[30318:[bind(A,$thf( c_emptyset ))]]) ).

thf(18733,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_emptyset != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,18690]) ).

thf(18734,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[18733]) ).

thf(18735,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[18734:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(5015,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_B ) ),
    inference(paramod_ordered,[status(thm)],[1883,370]) ).

thf(5016,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[5015]) ).

thf(5039,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_Message_Oagent_OSpy != c_emptyset )
      | ( c_0 != A )
      | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[5016]) ).

thf(5049,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_Message_Oagent_OSpy != c_emptyset )
      | ( c_0 != v_B ) ),
    inference(simp,[status(thm)],[5039]) ).

thf(246,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_1) ).

thf(957,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).

thf(894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(1027,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(22911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,623]) ).

thf(22912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22911]) ).

thf(22997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[22912]) ).

thf(23024,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[22997]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_0) ).

thf(454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(cnf,[status(esa)],[454]) ).

thf(456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(lifteq,[status(thm)],[455]) ).

thf(269,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(1012,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(45216,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36139]) ).

thf(45217,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45216]) ).

thf(45335,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45217]) ).

thf(45380,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45335]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[466]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5__iff1_0) ).

thf(566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(40,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(435,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff1_0) ).

thf(521,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(522,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[521]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff2_0) ).

thf(889,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).

thf(461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK__iff1_0) ).

thf(493,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(7693,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[435,491]) ).

thf(7694,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[7693]) ).

thf(7699,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[7694]) ).

thf(7713,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[7699]) ).

thf(51669,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36442]) ).

thf(51670,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51669]) ).

thf(51822,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51670]) ).

thf(51909,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51822]) ).

thf(38616,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36136]) ).

thf(38617,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38616]) ).

thf(38684,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38617]) ).

thf(38749,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ c_Message_Oparts )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) ) ),
    inference(simp,[status(thm)],[38684]) ).

thf(38511,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36136]) ).

thf(38512,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38511]) ).

thf(38718,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38512]) ).

thf(38786,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38718]) ).

thf(85,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(549,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(550,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[549]) ).

thf(551,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[550]) ).

thf(519,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[518]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(1143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5__iff1_0) ).

thf(650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(271,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(1017,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(312,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(1111,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(29441,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,476]) ).

thf(29442,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[29441]) ).

thf(29544,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[29442]) ).

thf(29598,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[29544]) ).

thf(51598,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36442]) ).

thf(51599,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51598]) ).

thf(51781,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51599]) ).

thf(51865,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51781]) ).

thf(211,axiom,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).

thf(869,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(498,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(cnf,[status(esa)],[497]) ).

thf(499,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[498]) ).

thf(51,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(463,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(8124,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[463,491]) ).

thf(8125,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[8124]) ).

thf(8128,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[8125]) ).

thf(8138,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[8128]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

thf(1089,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2__iff1_0) ).

thf(1138,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(4862,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[869,1151]) ).

thf(4863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4862]) ).

thf(4915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( A @ c_Event_OinitState )
       != c_emptyset )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != B ) ),
    inference(simp,[status(thm)],[4863]) ).

thf(4930,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != c_emptyset ),
    inference(simp,[status(thm)],[4915]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0) ).

thf(354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    inference(polarity_switch,[status(thm)],[354]) ).

thf(356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    inference(lifteq,[status(thm)],[355]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).

thf(933,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[552]) ).

thf(554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[553]) ).

thf(40928,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36137]) ).

thf(40929,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40928]) ).

thf(41044,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40929]) ).

thf(41124,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41044]) ).

thf(390,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Omsg_ONumber @ A )
      = B ),
    inference(detectInverse,[status(thm)],[389]) ).

thf(391,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_ONumber @ sk4 )
      = A ),
    inference(cnf,[status(esa)],[390]) ).

thf(1461,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_ONumber @ sk4 )
      = A ),
    inference(lifteq,[status(thm)],[391]) ).

thf(133,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(669,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(482,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Public_OpublicKey ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[481]) ).

thf(483,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk8 ) )
      = A ),
    inference(cnf,[status(esa)],[482]) ).

thf(11774,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk8 ) )
      = A ),
    inference(lifteq,[status(thm)],[483]) ).

thf(6623,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,2307]) ).

thf(6624,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6623]) ).

thf(6625,plain,
    ( ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6624:[bind(A,$thf( c_emptyset ))]]) ).

thf(49533,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36163]) ).

thf(49534,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49533]) ).

thf(49657,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49534]) ).

thf(49775,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49657]) ).

thf(28722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,1151]) ).

thf(28723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[28722]) ).

thf(28848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[28723]) ).

thf(28891,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[28848]) ).

thf(42814,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36138]) ).

thf(42815,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42814]) ).

thf(42869,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42815]) ).

thf(43005,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42869]) ).

thf(225,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_0) ).

thf(901,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6__iff1_0) ).

thf(1014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(1015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[1014]) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[1015]) ).

thf(100,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(590,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

thf(679,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(1039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(252,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( A @ ( D @ ( E @ ( F @ ( C @ v_sko__u8o ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OAgent @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OA__trusts__OR4__dest_0) ).

thf(970,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( A @ ( D @ ( E @ ( F @ ( C @ v_sko__u8o ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OAgent @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

thf(1155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(38604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36136]) ).

thf(38605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38604]) ).

thf(38689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38605]) ).

thf(38754,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[38689]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

thf(1131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(5862,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[4825,370]) ).

thf(5863,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[5862]) ).

thf(5886,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_A )
      | ( c_0 != A )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[5863]) ).

thf(5900,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_A )
      | ( c_Message_Oagent_OSpy != c_0 ) ),
    inference(simp,[status(thm)],[5886]) ).

thf(28276,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24734,476]) ).

thf(28277,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[28276]) ).

thf(28390,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) )
       != B ) ),
    inference(simp,[status(thm)],[28277]) ).

thf(28450,plain,
    ( ( ( tc_nat @ tc_set @ tc_set )
     != tc_Message_Omsg )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Finite__Set_OFinites ) ),
    inference(simp,[status(thm)],[28390]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(7218,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != c_Event_Obad )
      | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1661]) ).

thf(7219,plain,
    ! [A: $i] :
      ( ( A != c_Event_Obad )
      | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7218:[]]) ).

thf(7385,plain,
    ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7219]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(173,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(779,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(107,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(605,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(8597,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,8417]) ).

thf(8598,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[8597]) ).

thf(8599,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[8598:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(494,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[493]) ).

thf(22306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,494]) ).

thf(22307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22306]) ).

thf(22349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_nat )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_Message_OsymKeys )
      | ( A
       != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ) ),
    inference(simp,[status(thm)],[22307]) ).

thf(22375,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( c_UNIV @ c_Message_Oparts )
     != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[22349]) ).

thf(263,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(997,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(8672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
       != ( C @ ( B @ c_List_Orev ) ) )
      | ( ( c_List_Olist_ONil @ ( C @ sk5 ) )
        = B ) ),
    inference(paramod_ordered,[status(thm)],[347,8671]) ).

thf(8673,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ ( A @ sk5 ) )
      = c_List_Olist_ONil ),
    inference(pattern_uni,[status(thm)],[8672:[bind(A,$thf( A )),bind(B,$thf( c_List_Olist_ONil )),bind(C,$thf( A ))]]) ).

thf(6847,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_A )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,4801]) ).

thf(6848,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_A )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6847:[]]) ).

thf(7544,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( v_A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6848]) ).

thf(306,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).

thf(1099,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK__iff1_0) ).

thf(768,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(769,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[768]) ).

thf(4214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,769]) ).

thf(4215,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4214]) ).

thf(4233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_nat )
      | ( c_Message_OsymKeys != c_UNIV )
      | ( A
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(simp,[status(thm)],[4215]) ).

thf(4246,plain,
    c_Message_OsymKeys != c_UNIV,
    inference(simp,[status(thm)],[4233]) ).

thf(7133,plain,
    ! [A: $i] :
      ( ( A != c_Message_OsymKeys )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,4246]) ).

thf(7134,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7133:[bind(A,$thf( c_Message_OsymKeys ))]]) ).

thf(13144,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
      | ( c_UNIV != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7134]) ).

thf(13145,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[13144]) ).

thf(13181,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_Message_OsymKeys != c_0 )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[13145]) ).

thf(13192,plain,
    ( ( c_Message_OsymKeys != c_0 )
    | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[13181]) ).

thf(13595,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Message_OsymKeys != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,13192]) ).

thf(13596,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Message_OsymKeys != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[13595]) ).

thf(13597,plain,
    ( ( c_Message_OsymKeys != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[13596:[bind(A,$thf( c_UNIV ))]]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0) ).

thf(515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(792,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0) ).

thf(1086,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(508,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(lifteq,[status(thm)],[507]) ).

thf(14168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,494]) ).

thf(14169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14168]) ).

thf(14211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_nat )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Message_OsymKeys )
      | ( A
       != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ) ),
    inference(simp,[status(thm)],[14169]) ).

thf(14216,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( c_emptyset @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_insert ) ) )
     != c_Message_OsymKeys ),
    inference(simp,[status(thm)],[14211]) ).

thf(1166,plain,
    ( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[335,341]) ).

thf(1167,plain,
    ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1166]) ).

thf(1170,plain,
    ( ( tc_Message_Oagent != tc_Event_Oevent )
    | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != c_Event_Obad )
    | ( ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) )
     != v_A ) ),
    inference(simp,[status(thm)],[1167]) ).

thf(11975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[640,434]) ).

thf(11976,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[11975]) ).

thf(11977,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[11976:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OlessThan ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).

thf(12103,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) ),
    inference(simp,[status(thm)],[11977]) ).

thf(12419,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12103,491]) ).

thf(12420,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[12419]) ).

thf(12433,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[12420]) ).

thf(12442,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[12433]) ).

thf(23380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,623]) ).

thf(23381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23380]) ).

thf(23477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[23381]) ).

thf(23522,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[23477]) ).

thf(24002,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[23522]) ).

thf(11917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,434]) ).

thf(11918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[11917]) ).

thf(11919,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[11918:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OatMost ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).

thf(12074,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) ),
    inference(simp,[status(thm)],[11919]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(23407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,494]) ).

thf(23408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23407]) ).

thf(23464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_nat )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_Message_OsymKeys )
      | ( A
       != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ) ),
    inference(simp,[status(thm)],[23408]) ).

thf(23508,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
     != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[23464]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(1054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(871,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    inference(cnf,[status(esa)],[870]) ).

thf(872,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    inference(lifteq,[status(thm)],[871]) ).

thf(873,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Omsg_OKey @ A )
      = B ),
    inference(detectInverse,[status(thm)],[872]) ).

thf(874,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OKey @ sk29 )
      = A ),
    inference(cnf,[status(esa)],[873]) ).

thf(1466,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OKey @ sk29 )
      = A ),
    inference(lifteq,[status(thm)],[874]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(1071,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(45106,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
       != ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,36139]) ).

thf(45107,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45106]) ).

thf(45317,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent != A )
      | ( ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != c_Event_Obad )
      | ( c_Message_Oagent_OSpy != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45107]) ).

thf(45360,plain,
    ( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
     != c_Event_Obad )
    | ( c_Message_Oagent_OSpy != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45317]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(27195,plain,
    ( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ~ $true
    | ( c_emptyset != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[1572,1453]) ).

thf(27196,plain,
    ( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
     != ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[27195]) ).

thf(27225,plain,
    ( ( tc_nat != tc_nat )
    | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != c_0 )
    | ( c_0 != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[27196]) ).

thf(27236,plain,
    ( ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[27225]) ).

thf(14156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,1355]) ).

thf(14157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14156]) ).

thf(14201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( tc_nat @ ( tc_nat @ tc_prod ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Wellfounded__Relations_Oless__than )
      | ( A
       != ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
    inference(simp,[status(thm)],[14157]) ).

thf(14231,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
     != c_Wellfounded__Relations_Oless__than ),
    inference(simp,[status(thm)],[14201]) ).

thf(21260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[20021,460]) ).

thf(21261,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[21260]) ).

thf(21262,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[21261:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(21380,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_ONumber @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[21262]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).

thf(430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(cnf,[status(esa)],[523]) ).

thf(525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(lifteq,[status(thm)],[524]) ).

thf(526,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[525]) ).

thf(527,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( A @ sk11 ) )
      = B ),
    inference(cnf,[status(esa)],[526]) ).

thf(13455,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( A @ sk11 ) )
      = B ),
    inference(lifteq,[status(thm)],[527]) ).

thf(486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(cnf,[status(esa)],[485]) ).

thf(487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(lifteq,[status(thm)],[486]) ).

thf(488,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Message_OHPair ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[487]) ).

thf(489,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk9 ) )
      = A ),
    inference(cnf,[status(esa)],[488]) ).

thf(12982,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk9 ) )
      = A ),
    inference(lifteq,[status(thm)],[489]) ).

thf(9596,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,6796]) ).

thf(9597,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[9596]) ).

thf(9625,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_UNIV != c_0 )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[9597]) ).

thf(9635,plain,
    ( ( c_UNIV != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[9625]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(polarity_switch,[status(thm)],[571]) ).

thf(573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(lifteq,[status(thm)],[572]) ).

thf(12567,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7037]) ).

thf(12568,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[12567]) ).

thf(12601,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_Message_OsymKeys != c_0 )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[12568]) ).

thf(12609,plain,
    ( ( c_Message_OsymKeys != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[12601]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(1135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).

thf(750,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(12218,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[12074,491]) ).

thf(12219,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[12218]) ).

thf(12231,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[12219]) ).

thf(12238,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[12231]) ).

thf(42804,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36138]) ).

thf(42805,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42804]) ).

thf(42895,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42805]) ).

thf(42946,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ c_Message_Oparts )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) ) ),
    inference(simp,[status(thm)],[42895]) ).

thf(308,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ ( C @ ( B @ ( D @ v_sko__vEb ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OOR3__imp__OR2__dest_0) ).

thf(1103,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ ( C @ ( B @ ( D @ v_sko__vEb ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(49553,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36163]) ).

thf(49554,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49553]) ).

thf(49689,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49554]) ).

thf(49718,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49689]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(1288,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1159,340]) ).

thf(1289,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1288]) ).

thf(1301,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_Message_Oagent )
      | ( c_Message_OsymKeys != c_Event_Obad )
      | ( ( A @ c_Public_OshrK )
       != v_B ) ),
    inference(simp,[status(thm)],[1289]) ).

thf(40942,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36137]) ).

thf(40943,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40942]) ).

thf(41015,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40943]) ).

thf(41092,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41015]) ).

thf(138,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(689,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(19340,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[886,460]) ).

thf(19341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19340]) ).

thf(19342,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19341:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ c_Message_Omsg_OAgent )),bind(D,$thf( B ))]]) ).

thf(19403,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19342]) ).

thf(19479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19403,460]) ).

thf(19480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19479]) ).

thf(19481,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19480:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(19584,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19481]) ).

thf(19743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19584,460]) ).

thf(19744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[19743]) ).

thf(19745,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[19744:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(19861,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[19745]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).

thf(444,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK__iff1_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(1153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(polarity_switch,[status(thm)],[1152]) ).

thf(1154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(lifteq,[status(thm)],[1153]) ).

thf(154,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(732,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(22342,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,341]) ).

thf(22343,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22342]) ).

thf(22351,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Oagent )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_Event_Obad )
      | ( A != v_A ) ),
    inference(simp,[status(thm)],[22343]) ).

thf(22377,plain,
    ( ( tc_Message_Omsg != tc_Message_Oagent )
    | ( ( c_UNIV @ c_Message_Oparts )
     != c_Event_Obad ) ),
    inference(simp,[status(thm)],[22351]) ).

thf(171,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff2_0) ).

thf(772,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(6580,plain,
    ! [A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( c_0 != v_evs )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1447]) ).

thf(6581,plain,
    ( ( c_0 != v_evs )
    | ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6580:[bind(A,$thf( c_List_Olist_ONil ))]]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(579,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(26072,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,22261]) ).

thf(26073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26072]) ).

thf(26186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[26073]) ).

thf(26238,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[26186]) ).

thf(22025,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[869,465]) ).

thf(22026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ ( B @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22025]) ).

thf(22027,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22026:[bind(A,$thf( F )),bind(B,$thf( F @ c_Public_OshrK @ c_Message_Omsg_OKey )),bind(C,$thf( F @ c_Event_OinitState ))]]) ).

thf(22198,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(simp,[status(thm)],[22027]) ).

thf(30022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22198,1151]) ).

thf(30023,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[30022]) ).

thf(30138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( A @ c_Event_OinitState @ c_Message_Oparts )
       != c_emptyset )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != B ) ),
    inference(simp,[status(thm)],[30023]) ).

thf(30168,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != c_emptyset ),
    inference(simp,[status(thm)],[30138]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(1124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(562,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__injective__iff1_0) ).

thf(904,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(975,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(268,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_2) ).

thf(1007,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(139,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(694,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(26081,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,476]) ).

thf(26082,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26081]) ).

thf(26192,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[26082]) ).

thf(26245,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[26192]) ).

thf(1245,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[335,476]) ).

thf(1246,plain,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1245]) ).

thf(1252,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Event_Oevent )
      | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( v_K @ c_Message_Omsg_OKey @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( v_B_H @ c_Event_Oevent_OSays ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1246]) ).

thf(1256,plain,
    ( ( tc_Message_Omsg != tc_Event_Oevent )
    | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != ( c_emptyset @ c_Message_Oparts ) ) ),
    inference(simp,[status(thm)],[1252]) ).

thf(83,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(543,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(544,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[543]) ).

thf(545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(lifteq,[status(thm)],[544]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

thf(641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(23391,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,476]) ).

thf(23392,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23391]) ).

thf(23465,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[23392]) ).

thf(23509,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[23465]) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    inference(polarity_switch,[status(thm)],[934]) ).

thf(936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    inference(lifteq,[status(thm)],[935]) ).

thf(381,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(cnf,[status(esa)],[380]) ).

thf(382,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(lifteq,[status(thm)],[381]) ).

thf(38582,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36136]) ).

thf(38583,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38582]) ).

thf(38734,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38583]) ).

thf(38802,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38734]) ).

thf(49535,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36163]) ).

thf(49536,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49535]) ).

thf(49682,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49536]) ).

thf(49711,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49682]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(947,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(349,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Orev ) ) ) ),
    inference(cnf,[status(esa)],[348]) ).

thf(350,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[349]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).

thf(611,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(6793,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != v_A )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1187]) ).

thf(6794,plain,
    ( ( c_0 != v_A )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6793:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1__iff1_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(1057,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[1056]) ).

thf(1058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[1057]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(1107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(9473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1070,1151]) ).

thf(9474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[9473]) ).

thf(9537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != D )
      | ( ( B @ ( A @ c_Event_Oknows ) )
       != c_emptyset )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != C ) ),
    inference(simp,[status(thm)],[9474]) ).

thf(9538,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oknows ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[9537]) ).

thf(6498,plain,
    ! [A: $i] :
      ( ( A != c_Finite__Set_OFinites )
      | ( c_emptyset != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1409]) ).

thf(6499,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6498:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).

thf(7892,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,6499]) ).

thf(7893,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[7892]) ).

thf(7922,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_Finite__Set_OFinites != c_0 )
      | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[7893]) ).

thf(7928,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[7922]) ).

thf(7949,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_Finite__Set_OFinites != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,7928]) ).

thf(7950,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_Finite__Set_OFinites != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7949]) ).

thf(7951,plain,
    ( ( c_Finite__Set_OFinites != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7950:[bind(A,$thf( c_emptyset ))]]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = B )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_1) ).

thf(1092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = B )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_0) ).

thf(727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(cnf,[status(esa)],[727]) ).

thf(729,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(lifteq,[status(thm)],[728]) ).

thf(730,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[729]) ).

thf(731,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( B @ sk22 ) )
      = A ),
    inference(cnf,[status(esa)],[730]) ).

thf(14082,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( B @ sk22 ) )
      = A ),
    inference(lifteq,[status(thm)],[731]) ).

thf(51701,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36442]) ).

thf(51702,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51701]) ).

thf(51826,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51702]) ).

thf(51913,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ c_Message_Oparts )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) ) ),
    inference(simp,[status(thm)],[51826]) ).

thf(24501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,474]) ).

thf(24502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
      | ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24501]) ).

thf(24503,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[24502:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ c_SetInterval_OatMost ) )),bind(C,$thf( tc_nat ))]]) ).

thf(24817,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) ),
    inference(simp,[status(thm)],[24503]) ).

thf(4864,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[869,476]) ).

thf(4865,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4864]) ).

thf(4914,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( A @ c_Event_OinitState )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != B ) ),
    inference(simp,[status(thm)],[4865]) ).

thf(4929,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[4914]) ).

thf(45124,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36139]) ).

thf(45125,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45124]) ).

thf(45323,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45125]) ).

thf(45368,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45323]) ).

thf(4766,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 != v_A ) ),
    inference(paramod_ordered,[status(thm)],[1718,370]) ).

thf(4767,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4766]) ).

thf(4792,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_Message_Oagent_OSpy != c_emptyset )
      | ( c_0 != A )
      | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4767]) ).

thf(4805,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_Message_Oagent_OSpy != c_emptyset )
      | ( c_0 != v_A ) ),
    inference(simp,[status(thm)],[4792]) ).

thf(2153,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_evs )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1594]) ).

thf(2154,plain,
    ! [A: $i] :
      ( ( A != v_evs )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[2153:[]]) ).

thf(2171,plain,
    ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[2154]) ).

thf(4957,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,2171]) ).

thf(4958,plain,
    ( ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4957:[bind(A,$thf( tc_nat ))]]) ).

thf(1509,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( c_List_Olist_ONil @ c_List_Orev ) ) )
      | ( c_List_Olist_ONil = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,347]) ).

thf(1510,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil = c_0 )
      | ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Orev ) @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1509:[bind(A,$thf( D @ ( c_List_Olist_ONil @ c_List_Orev ) )),bind(B,$thf( D ))]]) ).

thf(2129,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil = c_0 )
      | ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Orev ) @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1510]) ).

thf(20179,plain,
    ( ( c_List_Olist_ONil = c_0 )
    | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(rewrite,[status(thm)],[2129,347]) ).

thf(106,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(603,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(604,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(lifteq,[status(thm)],[603]) ).

thf(174,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(784,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(40998,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36137]) ).

thf(40999,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40998]) ).

thf(41050,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40999]) ).

thf(41130,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41050]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_1) ).

thf(1117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(282,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = G )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_1) ).

thf(1048,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = G )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(22022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[615,465]) ).

thf(22023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22022]) ).

thf(22024,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[22023:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ c_Message_Omsg_ONumber )),bind(D,$thf( F @ c_Message_Osynth ))]]) ).

thf(22195,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    inference(simp,[status(thm)],[22024]) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,476]) ).

thf(1331,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1330]) ).

thf(1347,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != B ) ),
    inference(simp,[status(thm)],[1331]) ).

thf(1349,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_Message_Omsg )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Finite__Set_OFinites ) ),
    inference(simp,[status(thm)],[1347]) ).

thf(22286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,623]) ).

thf(22287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22286]) ).

thf(22356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[22287]) ).

thf(22382,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[22356]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

thf(450,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(cnf,[status(esa)],[450]) ).

thf(1606,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Event_Oevent @ tc_List_Olist ) )
      | ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,334]) ).

thf(1607,plain,
    ( ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
    | ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1606:[bind(A,$thf( tc_Event_Oevent @ tc_List_Olist ))]]) ).

thf(6294,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1607,423]) ).

thf(6295,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
      | ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[6294]) ).

thf(6327,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_Event_Oevent @ tc_List_Olist )
       != A )
      | ( c_0 != A )
      | ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[6295]) ).

thf(6340,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != c_0 )
    | ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[6327]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(46883,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36162]) ).

thf(46884,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46883]) ).

thf(46923,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46884]) ).

thf(47003,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46923]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(1043,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(317,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(1122,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(20214,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_List_Olist_ONil = c_0 )
      | ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,20179]) ).

thf(20215,plain,
    ( ( c_List_Olist_ONil = c_0 )
    | ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[20214:[bind(A,$thf( tc_nat ))]]) ).

thf(4499,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_UNIV != c_0 )
      | ( A != c_Event_Obad )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,4489]) ).

thf(4500,plain,
    ! [A: $i] :
      ( ( c_UNIV != c_0 )
      | ( A != c_Event_Obad )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4499:[]]) ).

thf(4509,plain,
    ( ( c_UNIV != c_0 )
    | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[4500]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(75,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(520,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1787,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_emptyset )
      | ( B @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,520]) ).

thf(1788,plain,
    ! [A: $i] :
      ( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1787:[bind(A,$thf( c_emptyset ))]]) ).

thf(2065,plain,
    ! [A: $i] :
      ( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1788]) ).

thf(362,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    inference(cnf,[status(esa)],[361]) ).

thf(363,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[362]) ).

thf(364,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ A ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[363]) ).

thf(365,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
      = A ),
    inference(cnf,[status(esa)],[364]) ).

thf(2180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[365]) ).

thf(166,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(758,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(cnf,[status(esa)],[533]) ).

thf(535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(lifteq,[status(thm)],[534]) ).

thf(9653,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,9635]) ).

thf(9654,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[9653]) ).

thf(9655,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[9654:[bind(A,$thf( c_emptyset ))]]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(6895,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_List_Olist_ONil != c_0 )
      | ( A != v_evs )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,2166]) ).

thf(6896,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil != c_0 )
      | ( A != v_evs )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6895:[]]) ).

thf(7551,plain,
    ( ( c_List_Olist_ONil != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( v_evs @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6896]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).

thf(1029,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(1338,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,341]) ).

thf(1339,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1338]) ).

thf(1344,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != tc_Message_Oagent )
      | ( c_Finite__Set_OFinites != c_Event_Obad )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != v_A ) ),
    inference(simp,[status(thm)],[1339]) ).

thf(58,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(477,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(209,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).

thf(865,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(4628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[865,476]) ).

thf(4629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4628]) ).

thf(4671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( B @ c_Event_Oused )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != C ) ),
    inference(simp,[status(thm)],[4629]) ).

thf(4694,plain,
    ! [A: $i] :
      ( ( A @ c_Event_Oused )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[4671]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(297,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).

thf(1080,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(7165,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1453]) ).

thf(7166,plain,
    ( ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7165:[bind(A,$thf( tc_nat ))]]) ).

thf(53055,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) )
      | ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7166]) ).

thf(53056,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) )
      | ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[53055]) ).

thf(53211,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( tc_nat != c_0 )
      | ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[53056]) ).

thf(53284,plain,
    ( ( tc_nat != c_0 )
    | ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[53211]) ).

thf(102,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).

thf(594,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(45198,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36139]) ).

thf(45199,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45198]) ).

thf(45320,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45199]) ).

thf(45364,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45320]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0) ).

thf(799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(38672,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36136]) ).

thf(38673,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38672]) ).

thf(38714,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38673]) ).

thf(38782,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38714]) ).

thf(29108,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_UNIV != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[1645,396]) ).

thf(29109,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
       != ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[29108]) ).

thf(29184,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
       != c_0 )
      | ( c_0 != A )
      | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[29109]) ).

thf(29189,plain,
    ( ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != c_0 )
    | ( c_UNIV != c_0 ) ),
    inference(simp,[status(thm)],[29184]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

thf(915,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(cnf,[status(esa)],[598]) ).

thf(600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(lifteq,[status(thm)],[599]) ).

thf(601,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[600]) ).

thf(602,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk15 ) )
      = B ),
    inference(cnf,[status(esa)],[601]) ).

thf(13486,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk15 ) )
      = B ),
    inference(lifteq,[status(thm)],[602]) ).

thf(462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[461]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(1061,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[397]) ).

thf(399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[398]) ).

thf(7029,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_Wellfounded__Relations_Oless__than != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1496]) ).

thf(7030,plain,
    ( ( c_Wellfounded__Relations_Oless__than != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7029:[bind(A,$thf( c_UNIV ))]]) ).

thf(1783,plain,
    ! [B: $i,A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( B @ ( c_0 @ c_lessequals ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,345]) ).

thf(1784,plain,
    ! [A: $i] :
      ( ( c_0 @ ( A @ ( c_0 @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1783:[bind(A,$thf( tc_nat ))]]) ).

thf(2064,plain,
    ! [A: $i] :
      ( ( c_0 @ ( A @ ( c_0 @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1784]) ).

thf(1172,plain,
    ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,851]) ).

thf(1173,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1172]) ).

thf(1176,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Oagent )
    | ( c_OtwayRees_Ootway != c_Event_Obad )
    | ( c_Message_Oagent_OServer != v_evs ) ),
    inference(simp,[status(thm)],[1173]) ).

thf(258,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(986,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

thf(1113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(49459,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36163]) ).

thf(49460,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49459]) ).

thf(49633,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49460]) ).

thf(49748,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49633]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_1) ).

thf(653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(229,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).

thf(827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).

thf(695,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(10195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[852,476]) ).

thf(10196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) ),
    inference(simp,[status(thm)],[10195]) ).

thf(10264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
       != D ) ),
    inference(simp,[status(thm)],[10196]) ).

thf(10275,plain,
    ! [A: $i] :
      ( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[10264]) ).

thf(289,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(1066,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(11850,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_Wellfounded__Relations_Oless__than != c_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[345,7030]) ).

thf(11851,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
       != ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[11850]) ).

thf(11885,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_nat )
      | ( A != c_0 )
      | ( c_UNIV != c_0 )
      | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[11851]) ).

thf(11889,plain,
    ( ( c_UNIV != c_0 )
    | ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
    inference(simp,[status(thm)],[11885]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(276,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(1034,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[424]) ).

thf(426,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) )
      | ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) )
        = A ) ),
    inference(lifteq,[status(thm)],[425]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4__iff1_0) ).

thf(944,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(905,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    inference(cnf,[status(esa)],[904]) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    inference(lifteq,[status(thm)],[905]) ).

thf(907,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Public_OshrK @ A )
      = B ),
    inference(detectInverse,[status(thm)],[906]) ).

thf(908,plain,
    ! [A: $i] :
      ( ( A @ c_Public_OshrK @ sk30 )
      = A ),
    inference(cnf,[status(esa)],[907]) ).

thf(1467,plain,
    ! [A: $i] :
      ( ( A @ c_Public_OshrK @ sk30 )
      = A ),
    inference(lifteq,[status(thm)],[908]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(14146,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,340]) ).

thf(14147,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14146]) ).

thf(14200,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_Message_Oagent )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Event_Obad )
      | ( A != v_B ) ),
    inference(simp,[status(thm)],[14147]) ).

thf(14230,plain,
    ( ( tc_Message_Oagent @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != c_Event_Obad ),
    inference(simp,[status(thm)],[14200]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1__iff1_0) ).

thf(1081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_0) ).

thf(939,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(1145,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
      = ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff2_0) ).

thf(968,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
      = ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(22840,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != c_UNIV ),
    inference(simp,[status(thm)],[22382]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(cnf,[status(esa)],[546]) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( A @ ( B @ c_append ) ) )
       != A ) ),
    inference(lifteq,[status(thm)],[547]) ).

thf(126,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(648,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(196,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3__iff1_0) ).

thf(836,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(51671,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36442]) ).

thf(51672,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51671]) ).

thf(51792,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51672]) ).

thf(51878,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51792]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(1025,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(24090,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,476]) ).

thf(24091,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24090]) ).

thf(24178,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[24091]) ).

thf(24228,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[24178]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(457,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[456]) ).

thf(458,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( B @ sk7 ) )
      = A ),
    inference(cnf,[status(esa)],[457]) ).

thf(11743,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( B @ sk7 ) )
      = A ),
    inference(lifteq,[status(thm)],[458]) ).

thf(22292,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,1355]) ).

thf(22293,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22292]) ).

thf(22350,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
       != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts )
       != c_Wellfounded__Relations_Oless__than )
      | ( A
       != ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) ) ) ),
    inference(simp,[status(thm)],[22293]) ).

thf(22376,plain,
    ( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
     != tc_Message_Omsg )
    | ( ( c_UNIV @ c_Message_Oparts )
     != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[22350]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(712,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).

thf(855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(51691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36442]) ).

thf(51692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51691]) ).

thf(51823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51692]) ).

thf(51910,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( v_B @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[51823]) ).

thf(580,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(lifteq,[status(thm)],[579]) ).

thf(16644,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ) )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,16584]) ).

thf(16645,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[16644]) ).

thf(16646,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[16645:[bind(A,$thf( E @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )),bind(B,$thf( E ))]]) ).

thf(16653,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[16646]) ).

thf(8247,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[732,491]) ).

thf(8248,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[8247]) ).

thf(8260,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[8248]) ).

thf(8263,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[8260]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(13119,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_Message_OsymKeys != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,12609]) ).

thf(13120,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_Message_OsymKeys != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[13119]) ).

thf(13121,plain,
    ( ( c_Message_OsymKeys != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[13120:[bind(A,$thf( c_emptyset ))]]) ).

thf(46826,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22192,36162]) ).

thf(46827,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46826]) ).

thf(46895,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Message_Oparts )
       != ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46827]) ).

thf(46971,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ c_Message_Oparts )
   != ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
    inference(simp,[status(thm)],[46895]) ).

thf(21085,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19861,460]) ).

thf(21086,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_in ) ) ) )
      | ( tc_Message_Omsg @ ( D @ c_Message_Osynth @ ( C @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(simp,[status(thm)],[21085]) ).

thf(21087,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(pattern_uni,[status(thm)],[21086:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash )),bind(D,$thf( A ))]]) ).

thf(21237,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_Message_Omsg_OHash @ c_in ) ) ),
    inference(simp,[status(thm)],[21087]) ).

thf(49626,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36163]) ).

thf(49627,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
    inference(simp,[status(thm)],[49626]) ).

thf(49659,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_emptyset ) ),
    inference(simp,[status(thm)],[49627]) ).

thf(49778,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_OsymKeys @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[49659]) ).

thf(14150,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,623]) ).

thf(14151,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14150]) ).

thf(14210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_Message_Omsg )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( D @ c_Event_OinitState @ c_Message_Oparts ) )
      | ( A
       != ( C @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[14151]) ).

thf(14215,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
     != ( B @ c_Event_OinitState @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[14210]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(5233,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( c_List_Olist_ONil != c_0 ) ),
    inference(paramod_ordered,[status(thm)],[2179,370]) ).

thf(5234,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( c_List_Olist_ONil != c_0 ) ),
    inference(simp,[status(thm)],[5233]) ).

thf(5255,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_evs )
      | ( c_0 != A )
      | ( c_List_Olist_ONil != c_0 ) ),
    inference(simp,[status(thm)],[5234]) ).

thf(5262,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( c_emptyset != v_evs )
      | ( c_List_Olist_ONil != c_0 ) ),
    inference(simp,[status(thm)],[5255]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(28720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,623]) ).

thf(28721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[28720]) ).

thf(28859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[28721]) ).

thf(28902,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[28859]) ).

thf(469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(cnf,[status(esa)],[468]) ).

thf(470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(lifteq,[status(thm)],[469]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).

thf(359,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(40908,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36137]) ).

thf(40909,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40908]) ).

thf(41041,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40909]) ).

thf(41121,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41041]) ).

thf(124,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(643,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(51689,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,36442]) ).

thf(51690,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51689]) ).

thf(51798,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51690]) ).

thf(51885,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51798]) ).

thf(5554,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_UNIV @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,4480]) ).

thf(5555,plain,
    ( ( c_0 @ ( c_UNIV @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[5554:[bind(A,$thf( tc_nat ))]]) ).

thf(22979,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,341]) ).

thf(22980,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22979]) ).

thf(22986,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Oagent )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
       != c_Event_Obad )
      | ( A != v_A ) ),
    inference(simp,[status(thm)],[22980]) ).

thf(23009,plain,
    ( ( tc_Message_Omsg != tc_Message_Oagent )
    | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
     != c_Event_Obad ) ),
    inference(simp,[status(thm)],[22986]) ).

thf(7012,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_evs )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1594]) ).

thf(7013,plain,
    ! [A: $i] :
      ( ( A != v_evs )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7012:[]]) ).

thf(7583,plain,
    ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( v_evs @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7013]) ).

thf(1953,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( ( B @ ( c_0 @ c_List_Oset ) )
        = c_emptyset )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1004]) ).

thf(1954,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_0 @ c_List_Oset ) )
        = c_emptyset )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1953:[bind(A,$thf( c_List_Olist_ONil ))]]) ).

thf(2113,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_0 @ c_List_Oset ) )
        = c_emptyset )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1954]) ).

thf(38626,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36136]) ).

thf(38627,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[38626]) ).

thf(38681,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[38627]) ).

thf(38746,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[38681]) ).

thf(415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[414]) ).

thf(9255,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
       != ( E @ tc_set @ ( C @ ( D @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( E @ tc_set @ ( D @ ( C @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[694,415]) ).

thf(9256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
       != ( E @ tc_set @ ( C @ ( D @ c_lessequals ) ) ) )
      | ~ ( E @ tc_set @ ( D @ ( C @ c_less ) ) ) ),
    inference(simp,[status(thm)],[9255]) ).

thf(9257,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
    inference(pattern_uni,[status(thm)],[9256:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(23457,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,341]) ).

thf(23458,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[23457]) ).

thf(23475,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Oagent )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_Event_Obad )
      | ( A != v_A ) ),
    inference(simp,[status(thm)],[23458]) ).

thf(23520,plain,
    ( ( tc_Message_Omsg != tc_Message_Oagent )
    | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
     != c_Event_Obad ) ),
    inference(simp,[status(thm)],[23475]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(46834,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,36162]) ).

thf(46835,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46834]) ).

thf(46942,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46835]) ).

thf(47022,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46942]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

thf(859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(500,plain,
    ? [A: $i > $i > $i > $i] :
    ! [B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
      = B ),
    inference(detectInverse,[status(thm)],[499]) ).

thf(501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk10 ) ) )
      = A ),
    inference(cnf,[status(esa)],[500]) ).

thf(29764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk10 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[501]) ).

thf(1247,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,476]) ).

thf(1248,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1247]) ).

thf(1253,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Oagent )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Event_Obad )
      | ( c_Message_Oagent_OSpy != A ) ),
    inference(simp,[status(thm)],[1248]) ).

thf(1257,plain,
    ( ( tc_Message_Omsg != tc_Message_Oagent )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Event_Obad ) ),
    inference(simp,[status(thm)],[1253]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(1141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(40910,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,36137]) ).

thf(40911,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40910]) ).

thf(41010,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40911]) ).

thf(41087,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[41010]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(11827,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( A != c_Message_Oagent_OServer )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,10394]) ).

thf(11828,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OSpy != c_0 )
      | ( A != c_Message_Oagent_OServer )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[11827:[]]) ).

thf(11830,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OServer @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[11828]) ).

thf(445,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(polarity_switch,[status(thm)],[444]) ).

thf(446,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(lifteq,[status(thm)],[445]) ).

thf(45196,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,36139]) ).

thf(45197,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45196]) ).

thf(45348,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45197]) ).

thf(45393,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[45348]) ).

thf(18104,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[16613,476]) ).

thf(18105,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[18104]) ).

thf(18242,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Wellfounded__Relations_Oless__than )
      | ( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
       != B ) ),
    inference(simp,[status(thm)],[18105]) ).

thf(18281,plain,
    ( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
     != tc_Message_Omsg )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[18242]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(1157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(96,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(581,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(495,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(1126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(383,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Omsg_ONonce @ A )
      = B ),
    inference(detectInverse,[status(thm)],[382]) ).

thf(384,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_ONonce @ sk3 )
      = A ),
    inference(cnf,[status(esa)],[383]) ).

thf(1448,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_ONonce @ sk3 )
      = A ),
    inference(lifteq,[status(thm)],[384]) ).

thf(42861,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36138]) ).

thf(42862,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[42861]) ).

thf(42914,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_UNIV ) ),
    inference(simp,[status(thm)],[42862]) ).

thf(42965,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[42914]) ).

thf(29120,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1645]) ).

thf(29121,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[29120]) ).

thf(29122,plain,
    ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[29121:[bind(A,$thf( c_UNIV ))]]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(539,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[538]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[366]) ).

thf(368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[367]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(46718,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,36162]) ).

thf(46719,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46718]) ).

thf(46904,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46719]) ).

thf(46980,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[46904]) ).

thf(1268,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,340]) ).

thf(1269,plain,
    ! [A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1268]) ).

thf(1276,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_Message_Oagent )
      | ( c_Finite__Set_OFinites != c_Event_Obad )
      | ( c_emptyset != v_B ) ),
    inference(simp,[status(thm)],[1269]) ).

thf(12542,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,11889]) ).

thf(12543,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_UNIV != c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[12542]) ).

thf(12544,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[12543:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(4626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[865,1151]) ).

thf(4627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[4626]) ).

thf(4679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != D )
      | ( ( B @ c_Event_Oused )
       != c_emptyset )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != C ) ),
    inference(simp,[status(thm)],[4627]) ).

thf(4681,plain,
    ! [A: $i] :
      ( ( A @ c_Event_Oused )
     != c_emptyset ),
    inference(simp,[status(thm)],[4679]) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[944]) ).

thf(946,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[945]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(polarity_switch,[status(thm)],[416]) ).

thf(418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(lifteq,[status(thm)],[417]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(99,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(588,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(699,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    inference(polarity_switch,[status(thm)],[515]) ).

thf(517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    inference(lifteq,[status(thm)],[516]) ).

thf(6752,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_0 != c_OtwayRees_Ootway )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1414]) ).

thf(6753,plain,
    ( ( c_0 != c_OtwayRees_Ootway )
    | ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6752:[bind(A,$thf( c_emptyset ))]]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(896,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(polarity_switch,[status(thm)],[650]) ).

thf(652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(lifteq,[status(thm)],[651]) ).

thf(25853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,22261]) ).

thf(25854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[25853]) ).

thf(25963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[25854]) ).

thf(26013,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[25963]) ).

thf(6908,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,5071]) ).

thf(6909,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6908]) ).

thf(6910,plain,
    ( ( tc_nat @ ( v_B @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6909:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(24081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23421,1151]) ).

thf(24082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[24081]) ).

thf(24190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[24082]) ).

thf(24242,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[24190]) ).

thf(1511,plain,
    ! [B: $i,A: $i] :
      ( ( A != c_List_Olist_ONil )
      | ( ( B @ ( c_0 @ c_List_Orev ) )
        = c_List_Olist_ONil )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,347]) ).

thf(1512,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_0 @ c_List_Orev ) )
        = c_List_Olist_ONil )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( c_List_Olist_ONil ))]]) ).

thf(2130,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_0 @ c_List_Orev ) )
        = c_List_Olist_ONil )
      | ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[1512]) ).

thf(567,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    inference(polarity_switch,[status(thm)],[566]) ).

thf(568,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    inference(lifteq,[status(thm)],[567]) ).

thf(29873,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[29598]) ).

thf(235,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(929,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(536,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[509]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(478,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[477]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).

thf(763,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(224,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(264,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0) ).

thf(999,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(1577,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,492]) ).

thf(1578,plain,
    ( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[1577:[bind(A,$thf( tc_nat ))]]) ).

thf(431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(cnf,[status(esa)],[430]) ).

thf(432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[431]) ).

thf(40930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36137]) ).

thf(40931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[40930]) ).

thf(41013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[40931]) ).

thf(41090,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_Message_Oagent_OSpy @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[41013]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(1133,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).

thf(839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(cnf,[status(esa)],[839]) ).

thf(841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(lifteq,[status(thm)],[840]) ).

thf(842,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[841]) ).

thf(843,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk28 ) )
      = A ),
    inference(cnf,[status(esa)],[842]) ).

thf(18914,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk28 ) )
      = A ),
    inference(lifteq,[status(thm)],[843]) ).

thf(14166,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,769]) ).

thf(14167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14166]) ).

thf(14199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_nat )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Message_OsymKeys )
      | ( A
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(simp,[status(thm)],[14167]) ).

thf(14229,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( c_emptyset @ ( B @ ( A @ c_Public_OpublicKey ) @ c_insert ) ) )
     != c_Message_OsymKeys ),
    inference(simp,[status(thm)],[14199]) ).

thf(1340,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,491]) ).

thf(1341,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1340]) ).

thf(1345,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != ( tc_nat @ tc_set ) )
      | ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != c_UNIV ) ),
    inference(simp,[status(thm)],[1341]) ).

thf(1348,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[1345]) ).

thf(27146,plain,
    ( ( c_emptyset != c_emptyset )
    | ( c_0 != c_0 )
    | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13195,1572]) ).

thf(27147,plain,
    ( ( c_emptyset != c_emptyset )
    | ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[27146]) ).

thf(27148,plain,
    ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[27147:[]]) ).

thf(1270,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[721,851]) ).

thf(1271,plain,
    ! [A: $i] :
      ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1270]) ).

thf(1280,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_Message_Oagent )
      | ( c_Finite__Set_OFinites != c_Event_Obad )
      | ( c_emptyset != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[1271]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).

thf(950,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(1097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).

thf(564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(6428,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_A )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1718]) ).

thf(6429,plain,
    ! [A: $i] :
      ( ( A != v_A )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6428:[]]) ).

thf(7433,plain,
    ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( v_A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6429]) ).

thf(506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[505]) ).

thf(358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(cnf,[status(esa)],[357]) ).

thf(14152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,1151]) ).

thf(14153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14152]) ).

thf(14209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != D )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_emptyset )
      | ( A != C ) ),
    inference(simp,[status(thm)],[14153]) ).

thf(14214,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
     != c_emptyset ),
    inference(simp,[status(thm)],[14209]) ).

thf(22316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22081,342]) ).

thf(22317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22316]) ).

thf(22364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Event_Oevent )
      | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
       != ( c_UNIV @ c_Message_Oparts ) )
      | ( A
       != ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( B @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(simp,[status(thm)],[22317]) ).

thf(22392,plain,
    ( ( tc_Message_Omsg != tc_Event_Oevent )
    | ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
     != ( c_UNIV @ c_Message_Oparts ) ) ),
    inference(simp,[status(thm)],[22364]) ).

thf(1334,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[484,340]) ).

thf(1335,plain,
    ! [A: $i] :
      ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1334]) ).

thf(1346,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ tc_set )
       != tc_Message_Oagent )
      | ( c_Finite__Set_OFinites != c_Event_Obad )
      | ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
       != v_B ) ),
    inference(simp,[status(thm)],[1335]) ).

thf(25825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,22261]) ).

thf(25826,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[25825]) ).

thf(25954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != tc_Message_Omsg )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( D @ c_Event_OinitState ) )
      | ( A
       != ( C @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[25826]) ).

thf(26007,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
     != ( B @ c_Event_OinitState ) ),
    inference(simp,[status(thm)],[25954]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(polarity_switch,[status(thm)],[799]) ).

thf(801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(lifteq,[status(thm)],[800]) ).

thf(26770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22193,476]) ).

thf(26771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26770]) ).

thf(26861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( B @ c_Message_Osynth @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Message_Omsg_OAgent )
       != C ) ),
    inference(simp,[status(thm)],[26771]) ).

thf(26898,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[26861]) ).

thf(1192,plain,
    ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,491]) ).

thf(1193,plain,
    ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1192]) ).

thf(1197,plain,
    ( ( ( tc_nat @ tc_set )
     != ( tc_Event_Oevent @ tc_List_Olist ) )
    | ( c_Finite__Set_OFinites != c_OtwayRees_Ootway )
    | ( c_UNIV != v_evs ) ),
    inference(simp,[status(thm)],[1193]) ).

thf(2193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[615,1151]) ).

thf(2194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2193]) ).

thf(2219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != D )
      | ( ( B @ c_Message_Osynth )
       != c_emptyset )
      | ( ( A @ c_Message_Omsg_ONumber )
       != C ) ),
    inference(simp,[status(thm)],[2194]) ).

thf(2223,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth )
     != c_emptyset ),
    inference(simp,[status(thm)],[2219]) ).

thf(5181,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ~ $true
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2299,370]) ).

thf(5182,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
       != ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5181]) ).

thf(5203,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_set )
       != tc_nat )
      | ( c_emptyset != c_emptyset )
      | ( c_0 != A )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5182]) ).

thf(5215,plain,
    ! [A: $i] :
      ( ( ( A @ tc_set )
       != tc_nat )
      | ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[5203]) ).

thf(46698,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[962,36162]) ).

thf(46699,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46698]) ).

thf(46936,plain,
    ! [A: $i] :
      ( ( A != tc_Message_Oagent )
      | ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != c_Event_Obad )
      | ( c_Message_OsymKeys != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[46699]) ).

thf(47016,plain,
    ( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
     != c_Event_Obad )
    | ( c_Message_OsymKeys != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[46936]) ).

thf(654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(cnf,[status(esa)],[653]) ).

thf(655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(lifteq,[status(thm)],[654]) ).

thf(656,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( B @ A ) )
      = C ),
    inference(detectInverse,[status(thm)],[655]) ).

thf(657,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( A @ sk16 ) )
      = B ),
    inference(cnf,[status(esa)],[656]) ).

thf(13517,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( A @ sk16 ) )
      = B ),
    inference(lifteq,[status(thm)],[657]) ).

thf(23307,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState )
     != ( c_UNIV @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[23024]) ).

thf(1162,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[334,341]) ).

thf(1163,plain,
    ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1162]) ).

thf(1165,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Oagent )
    | ( c_OtwayRees_Ootway != c_Event_Obad )
    | ( v_evs != v_A ) ),
    inference(simp,[status(thm)],[1163]) ).

thf(6950,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,4509]) ).

thf(6951,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6950]) ).

thf(6952,plain,
    ( ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6951:[bind(A,$thf( c_UNIV ))]]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(1129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(104,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(18717,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_emptyset != c_0 )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,18690]) ).

thf(18718,plain,
    ! [A: $i] :
      ( ( A != c_Wellfounded__Relations_Oless__than )
      | ( c_emptyset != c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(simp,[status(thm)],[18717]) ).

thf(18719,plain,
    ( ( c_emptyset != c_0 )
    | ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[18718:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).

thf(7086,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != c_0 )
      | ( c_0 != v_B )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,5047]) ).

thf(7087,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != v_B )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7086]) ).

thf(7088,plain,
    ( ( c_0 != v_B )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7087:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(1292,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1159,341]) ).

thf(1293,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[1292]) ).

thf(1299,plain,
    ! [A: $i] :
      ( ( tc_nat != tc_Message_Oagent )
      | ( c_Message_OsymKeys != c_Event_Obad )
      | ( ( A @ c_Public_OshrK )
       != v_A ) ),
    inference(simp,[status(thm)],[1293]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(624,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(26759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
       != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22193,1151]) ).

thf(26760,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
     != ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26759]) ).

thf(26853,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != D )
      | ( ( B @ c_Message_Osynth @ c_Message_Oparts )
       != c_emptyset )
      | ( ( A @ c_Message_Omsg_OAgent )
       != C ) ),
    inference(simp,[status(thm)],[26760]) ).

thf(26893,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
     != c_emptyset ),
    inference(simp,[status(thm)],[26853]) ).

thf(22922,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,476]) ).

thf(22923,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22922]) ).

thf(22989,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[22923]) ).

thf(23013,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[22989]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_0) ).

thf(822,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(6663,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( A != v_B )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,1883]) ).

thf(6664,plain,
    ! [A: $i] :
      ( ( A != v_B )
      | ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6663:[]]) ).

thf(7493,plain,
    ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( v_B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6664]) ).

thf(6593,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( c_0 != c_0 )
      | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,4825]) ).

thf(6594,plain,
    ! [A: $i] :
      ( ( A != c_Message_Oagent_OSpy )
      | ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[6593]) ).

thf(6595,plain,
    ( ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
    | ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[6594:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).

thf(4712,plain,
    ! [A: $i] :
      ( ( A != tc_nat )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
      | ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(paramod_ordered,[status(thm)],[402,1514]) ).

thf(4713,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
    | ( c_0 @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
    | ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
    inference(pattern_uni,[status(thm)],[4712:[bind(A,$thf( tc_nat ))]]) ).

thf(46814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36162]) ).

thf(46815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Message_OsymKeys @ c_in ) ) ) ),
    inference(simp,[status(thm)],[46814]) ).

thf(46916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[46815]) ).

thf(46995,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[46916]) ).

thf(22913,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,1151]) ).

thf(22914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22913]) ).

thf(22987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != C )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
       != c_emptyset )
      | ( A != B ) ),
    inference(simp,[status(thm)],[22914]) ).

thf(23010,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
   != c_emptyset ),
    inference(simp,[status(thm)],[22987]) ).

thf(30033,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22198,476]) ).

thf(30034,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[30033]) ).

thf(30121,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( A @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
       != B ) ),
    inference(simp,[status(thm)],[30034]) ).

thf(30155,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[30121]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

thf(1120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(28733,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26115,476]) ).

thf(28734,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
    inference(simp,[status(thm)],[28733]) ).

thf(28843,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[28734]) ).

thf(28886,plain,
    ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[28843]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(14191,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,341]) ).

thf(14192,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14191]) ).

thf(14207,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_Message_Oagent )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Event_Obad )
      | ( A != v_A ) ),
    inference(simp,[status(thm)],[14192]) ).

thf(14237,plain,
    ( ( tc_Message_Oagent @ ( c_emptyset @ ( v_A @ c_insert ) ) )
   != c_Event_Obad ),
    inference(simp,[status(thm)],[14207]) ).

thf(51761,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22950,36442]) ).

thf(51762,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( B @ ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
    inference(simp,[status(thm)],[51761]) ).

thf(51782,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg != B )
      | ( ( B @ ( c_emptyset @ ( v_B @ c_insert ) ) )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A != c_Message_Oagent_OSpy ) ),
    inference(simp,[status(thm)],[51762]) ).

thf(51866,plain,
    ( ( tc_Message_Omsg @ ( c_emptyset @ ( v_B @ c_insert ) ) )
   != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[51782]) ).

thf(764,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    inference(cnf,[status(esa)],[763]) ).

thf(765,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    inference(lifteq,[status(thm)],[764]) ).

thf(766,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Oagent_OFriend @ A )
      = B ),
    inference(detectInverse,[status(thm)],[765]) ).

thf(767,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend @ sk24 )
      = A ),
    inference(cnf,[status(esa)],[766]) ).

thf(1463,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend @ sk24 )
      = A ),
    inference(lifteq,[status(thm)],[767]) ).

thf(7089,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_B )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,5047]) ).

thf(7090,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OSpy != c_0 )
      | ( A != v_B )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[7089:[]]) ).

thf(7602,plain,
    ( ( c_Message_Oagent_OSpy != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( v_B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7090]) ).

thf(88,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(560,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(26068,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24122,623]) ).

thf(26069,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(simp,[status(thm)],[26068]) ).

thf(26177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( C @ c_Event_OinitState @ c_Message_Oparts )
       != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) )
      | ( A
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(simp,[status(thm)],[26069]) ).

thf(26225,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts )
     != ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[26177]) ).

thf(1030,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    inference(cnf,[status(esa)],[1029]) ).

thf(1031,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    inference(lifteq,[status(thm)],[1030]) ).

thf(1032,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Message_Omsg_OAgent @ A )
      = B ),
    inference(detectInverse,[status(thm)],[1031]) ).

thf(1033,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OAgent @ sk36 )
      = A ),
    inference(cnf,[status(esa)],[1032]) ).

thf(1468,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Omsg_OAgent @ sk36 )
      = A ),
    inference(lifteq,[status(thm)],[1033]) ).

thf(2,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(337,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14307,plain,
    ! [A: $i] :
      ( ( c_0 != c_0 )
      | ( c_emptyset != c_0 )
      | ( A != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[405,13671]) ).

thf(14308,plain,
    ! [A: $i] :
      ( ( c_emptyset != c_0 )
      | ( A != c_Event_Obad )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[14307:[]]) ).

thf(14310,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[14308]) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(polarity_switch,[status(thm)],[1086]) ).

thf(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(lifteq,[status(thm)],[1087]) ).

thf(22936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
       != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22320,494]) ).

thf(22937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(simp,[status(thm)],[22936]) ).

thf(22995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg != tc_nat )
      | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
       != c_Message_OsymKeys )
      | ( A
       != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ) ),
    inference(simp,[status(thm)],[22937]) ).

thf(23022,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( c_UNIV @ c_Message_Oparts @ c_Message_Oparts )
     != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[22995]) ).

thf(496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(cnf,[status(esa)],[495]) ).

thf(1068,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    inference(polarity_switch,[status(thm)],[1067]) ).

thf(1069,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    inference(lifteq,[status(thm)],[1068]) ).

thf(14170,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
       != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[757,851]) ).

thf(14171,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[14170]) ).

thf(14206,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_Message_Oagent )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != c_Event_Obad )
      | ( A != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[14171]) ).

thf(14236,plain,
    ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
   != c_Event_Obad ),
    inference(simp,[status(thm)],[14206]) ).

thf(45218,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
       != ( C @ ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1102,36139]) ).

thf(45219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
     != ( C @ ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
    inference(simp,[status(thm)],[45218]) ).

thf(45312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
       != c_UNIV )
      | ( A != c_Wellfounded__Relations_Oless__than ) ),
    inference(simp,[status(thm)],[45219]) ).

thf(45353,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
     != c_UNIV ),
    inference(simp,[status(thm)],[45312]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).

thf(972,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(68836,plain,
    $false,
    inference(e,[status(thm)],[645,1036,26250,1718,629,760,347,846,909,518,941,666,479,1105,962,468,481,352,18691,8417,523,1005,36162,6695,42927,22193,1073,45366,13424,449,379,511,7516,18951,22424,408,14235,46976,13548,6796,2248,1041,861,1078,385,39011,533,8568,16613,1164,715,472,2168,6551,42959,538,47018,36137,6727,7484,1327,41101,5178,1063,340,1196,22379,1001,46966,1576,1441,42968,43004,436,28907,829,1095,709,13251,18321,885,1046,1645,36136,8671,49764,22320,51914,1298,719,372,504,24971,6066,619,1279,49704,14228,7386,389,1409,724,38759,785,802,344,934,357,1462,1059,542,460,817,853,26474,1514,1572,22374,23026,5076,1147,6396,421,870,16584,18988,49781,770,881,416,1115,5052,2222,1415,24734,591,443,18273,1109,10271,623,5804,514,22261,806,353,475,924,492,13195,54196,1302,42944,20021,485,834,1151,937,574,1020,348,14232,1283,1051,45369,397,877,1447,453,774,18639,4825,45423,4588,507,12090,19717,634,6755,734,49774,866,14113,396,38744,411,988,9556,13671,380,512,26435,661,4480,7037,29586,810,7269,1067,7533,452,42967,546,41116,26993,18312,36163,366,2296,2307,798,49712,910,1091,825,952,1355,1255,598,7834,392,18690,424,23514,429,10394,815,30319,18735,1883,5049,334,957,894,22383,361,879,1027,757,23024,456,1012,45380,467,566,484,852,435,583,522,889,2179,1159,461,493,7713,51909,38749,38786,551,519,1143,650,1017,615,1328,24240,1111,403,29598,51865,869,499,8138,857,697,1089,1138,4930,356,471,1329,1659,933,554,41124,1461,669,1414,637,11774,6625,49775,28891,30279,339,43005,901,686,1075,476,1016,590,679,1039,970,1155,38754,622,1324,738,1131,5900,28450,984,721,7385,569,779,371,605,8599,22375,997,8673,7544,1099,13597,515,1150,343,792,1086,508,14216,1170,12442,530,24002,12074,921,23508,1054,1466,1071,1187,674,45360,794,586,27236,14231,21380,430,13455,12982,9635,573,12609,1135,965,750,618,12238,42946,1103,49718,745,1301,41092,689,19861,444,4489,375,733,1154,423,402,732,22377,772,7134,6581,4801,875,579,26238,30168,1124,562,904,975,1007,694,743,26245,1256,545,641,23509,936,382,38802,23421,49711,804,704,947,350,540,611,22081,787,6794,1058,1107,9538,7951,466,1092,14082,335,2166,51913,22422,24817,5071,406,4929,681,419,2299,45368,4805,4958,20179,6460,979,604,784,41130,1117,1048,736,22195,1349,22382,451,6340,509,47003,1043,434,616,1122,20215,4509,863,2065,2180,758,535,9655,609,7551,1029,1344,769,7023,477,4694,811,387,494,1080,53284,345,552,594,45364,799,38782,29189,7928,848,520,626,915,13486,462,1061,399,7030,1594,2171,883,2064,1176,986,1113,49748,653,658,912,521,768,827,695,10275,1066,868,1496,24122,851,1102,505,438,11889,722,1034,490,426,944,1467,16089,927,14230,1081,939,342,1145,968,22840,1413,473,663,548,648,487,836,51878,5047,525,1025,1070,24228,414,11743,22376,409,712,557,1003,855,51910,580,7166,16653,640,8263,19416,707,12103,887,13121,22192,46971,23522,21237,49778,19584,14215,993,5262,791,441,370,717,28902,338,470,359,36139,41121,643,51885,1188,5555,502,23009,463,7583,808,336,2113,38746,4246,9257,727,23520,595,47022,497,859,991,29764,1257,1141,41087,613,11830,446,571,45393,363,18281,1157,581,495,891,1126,1448,36442,42965,465,450,29122,1084,931,539,976,26115,368,844,1453,6711,46980,1276,12544,813,4681,36138,946,632,418,995,588,699,963,517,6753,4806,896,748,652,351,26013,6910,24242,2130,568,378,19403,29873,929,832,549,22198,536,433,510,1077,478,1607,763,899,1661,346,2294,6462,6499,999,752,447,1578,432,967,13192,405,41090,865,1133,18914,14229,1348,27148,1280,950,1097,422,790,373,603,564,7433,341,506,358,36443,14214,1056,22392,1346,26007,796,918,801,474,1410,26898,400,1197,2223,5215,47016,13517,23307,1165,6952,886,415,740,464,1129,596,459,18719,7088,850,1004,1299,395,624,839,1152,427,1384,26893,528,23013,822,7493,6595,4713,46995,442,23010,30155,1120,28886,369,607,14237,354,51866,1463,543,7602,560,26225,22950,1468,337,14310,491,1088,23022,496,454,1069,14236,45353,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWV286-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/5.38  % Computer : n012.cluster.edu
% 0.08/5.38  % Model    : x86_64 x86_64
% 0.08/5.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38  % Memory   : 8046.5625MB
% 0.08/5.38  % OS       : Linux 6.8.0-71-generic
% 0.08/5.38  % CPULimit : 300
% 0.08/5.38  % WCLimit  : 300
% 0.08/5.38  % DateTime : Sat Sep 26 13:27:39 UTC 2026
% 0.08/5.38  % CPUTime  : 
% 0.08/5.38  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/5.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/6.29  % [INFO] 	 Parsing done (356ms). 
% 1.52/6.30  % [INFO] 	 Running in sequential loop mode. 
% 2.00/6.63  % [INFO] 	 eprover registered as external prover. 
% 2.00/6.64  % [INFO] 	 Scanning for conjecture ... 
% 2.39/6.83  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1476 axioms. Running axiom selection ... 
% 2.92/7.11  % [INFO] 	 Axiom selection finished. Selected 327 axioms (removed 1149 axioms). 
% 3.58/7.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.58/7.33  % [INFO] 	 Type checking passed. 
% 3.58/7.33  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 76.14/27.59  % External prover 'e' found a proof!
% 76.14/27.59  % [INFO] 	 Killing All external provers ... 
% 76.14/27.59  % Time passed: 22038ms (effective reasoning time: 21280ms)
% 76.14/27.60  % Axioms used in derivation (327): cls_List_Olistrel__Cons1_0, cls_Message_Omsg_Oinject__7__iff1_0, cls_Finite__Set_Ofinite__Union_0, cls_List_Oset__empty2__iff2_0, cls_Public_Onot__symKeys__pubK__iff1_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_Message_Oanalz_OInj_0, cls_List_Ofinite__set_0, cls_List_Orev__is__Nil__conv__iff1_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_List_Oset__empty2__iff1_0, cls_Event_OSays__imp__analz__Spy__dest_0, cls_Public_OpublicKey__into__used_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Public_ONonce__notin__initState__iff1_0, cls_Event_Oevent_Odistinct__3__iff1_0, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Olength__remdups__eq__iff2_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_Message_OMPair__eq__HPair__iff1_1, cls_List_ONil__is__append__conv__iff2_0, cls_Message_Osynth_OAgent_0, cls_Event_Oevent_Odistinct__1__iff1_0, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Finite__Set_OFinites_OemptyI_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Event_Oevent_Oinject__3__iff1_0, cls_Message_Oagent_Odistinct__5__iff1_0, cls_Message_Oagent_Oinject__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_List_Orev__eq__Cons__iff__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Public_OpriK__neq__shrK__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Message_OHPair__neqs__1__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Message_OHPair__neqs__3__iff1_0, cls_Nat_Oless__irrefl_0, cls_Event_Oevent_Oinject__1__iff1_2, cls_List_Olistrel__Nil1_0, cls_Nat_Onot__less0__iff1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Message_OMPair__synth__analz__iff1_1, cls_Public_OshrK_AX_A_58_AsymKeys_0, cls_Message_OHPair__eq__iff1_0, cls_Finite__Set_Ofinite__Int_0, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, cls_Infinite__Set_Onat__not__finite_0, cls_Message_Osynth_OHash_0, cls_Message_OMPair__eq__HPair__iff1_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Message_Oagent_Odistinct__6__iff1_0, cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, cls_Relation_ORangeE_0, cls_Message_Osynth_ONumber_0, cls_Set_OInterI_1, cls_Message_Omsg_Oinject__7__iff1_1, cls_List_Oset__empty__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0, cls_Set_OUnCI_1, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Message_Oparts_OInj_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_List_Olength__remdups__leq_0, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, cls_Event_Oevent_Oinject__3__iff1_1, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Public_OMPair__used_1, cls_Set_OPow__iff__iff2_0, cls_Message_OHPair__eq__MPair__iff1_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Message_OCrypt__synth_1, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Public_OsymKeys__invKey__iff__iff1_0, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Set_Onot__psubset__empty__iff1_0, cls_Message_Osynth_OMPair_0, cls_Set_OUnE_0, cls_List_Olistrel__Cons2_0, cls_Message_OHPair__eq__MPair__iff2_0, cls_Message_Omsg_Oinject__4__iff1_0, cls_Set_OinsertE_0, cls_Message_Oagent_Odistinct__2__iff1_0, cls_List_Owf__lex_0, cls_List_Orev__is__Nil__conv__iff2_0, cls_Set_OUn__empty__iff1_1, cls_Public_OpublicKey__inject__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Message_Omsg_Oinject__3__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Message_OHPair__neqs__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Event_Oevent_Oinject__2__iff1_0, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_List_Oin__listsI_1, cls_List_Orev__eq__Cons__iff__iff1_0, cls_Message_Oagent_Odistinct__1__iff1_0, cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Message_OMPair__eq__HPair__iff2_0, cls_Message_Oparts_OBody__dest_0, cls_Datatype__Universe_OuprodE_2, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Public_OshrK__in__used_0, cls_Message_Omsg_Oinject__5__iff1_0, cls_Datatype__Universe_OuprodE_0, cls_Public_OMPair__used_0, cls_Set_ODiffE_0, cls_Public_OshrK__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Message_OHPair__neqs__6__iff1_0, cls_Message_Oin__parts__UnE_0, cls_OtwayRees_OGets__imp__Says__dest_0, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Message_OMPair__analz_1, cls_Datatype__Universe_OdprodE_2, cls_Public_OpublicKey__inject__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Message_OCrypt__synth_0, cls_List_Odistinct__remdups_0, cls_Finite__Set_Ofinite__Union_1, cls_Message_Omsg_Oinject__2__iff1_0, cls_Event_Oevent_Oinject__1__iff1_0, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Set_OIntI_0, cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Message_Omsg_Oinject__6__iff1_0, cls_Public_Oanalz__spies__pubK_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Public_Onot__symKeys__priK__iff1_0, cls_Event_Oevent_Odistinct__5__iff1_0, cls_Message_OMPair__parts_1, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OMPair__synth__analz__iff1_0, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Message_Oagent_Odistinct__4__iff1_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_Message_Osynth__synthD__dest_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_Public_OSpy__spies__bad__shrK_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_Set_ODiffI_0, cls_Public_OpublicKey__neq__privateKey__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, cls_OtwayRees_OOR3__imp__OR2__dest_0, cls_List_Oappend__self__conv__iff2_0, cls_Message_ONonce__synth_0, cls_List_Orev__is__rev__conv__iff1_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_List_Olistrel__Nil2_0, cls_Message_OHPair__neqs__5__iff1_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_OtwayRees_Ounique__NB__dest_1, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Event_Oevent_Oinject__2__iff1_1, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Message_OMPair__synth__analz__iff2_0, cls_Relation_OdiagE_1, cls_Message_Oanalz__into__parts__dest_0, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_Message_OMPair__synth_1, cls_Message_OHPair__eq__MPair__iff1_1, cls_List_Olist_Odistinct__1__iff1_0, cls_Public_Ospies__pubK_0, cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, cls_List_Olistrel__Cons1_1, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_Message_Osynth_OInj_0, cls_List_ONil__is__rev__conv__iff2_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_Sum__Type_OPlusE_1, cls_Event_Oevent_Odistinct__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_Event_Oevent_Odistinct__6__iff1_0, cls_Message_Omsg_Oinject__6__iff1_1, cls_Message_Oagent_Odistinct__3__iff1_0, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_OHPair__neqs__2__iff1_0, cls_Public_OpriK__in__initState_0, cls_Message_OHPair__eq__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, cls_Message_OKey__synth_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_Public_OpublicKey__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_0, cls_Event_OSpy_A_58_Abad_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_List_ONil__is__rev__conv__iff1_0, cls_Event_Oevent_Oinject__1__iff1_1, cls_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_OtwayRees_OSpy__see__shrK__D__dest_0, cls_List_Olength__0__conv__iff1_0, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Message_Oparts__emptyE_0, cls_Set_OpsubsetE_1, cls_Public_OshrK__injective__iff1_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, cls_OtwayRees_Ounique__NB__dest_0, cls_Relation_Orel__compE_1, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Event_Oevent_Odistinct__2__iff1_0, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Public_OsymKeys__invKey__iff__iff2_0, cls_List_Olength__remdups__eq__iff1_0, cls_Message_OMPair__synth_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Public_OpubK__neq__shrK__iff1_0, cls_OtwayRees_OA__trusts__OR4__dest_0, cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0, cls_Public_OshrK__in__knows_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 76.14/27.60  % No. of inferences in proof: 2070
% 76.14/27.60  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 22038 ms resp. 21280 ms w/o parsing
% 77.36/27.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.36/27.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------