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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV337-1 : 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 : n026.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 08:59:01 AM UTC 2026

% Result   : Unsatisfiable 148.81s 42.57s
% Output   : Refutation 149.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :  899
% Syntax   : Number of formulae    : 1908 ( 513 unt;   0 typ;   1 def)
%            Number of atoms       : 3570 ( 639 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 14119 (1759   ~;1585   |;   0   &;10775   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  194 ( 191 usr;  27 con; 0-6 aty)
%            Number of variables   : 3281 (   0   ^;3279   !;   1   ?;3281   :)
%                                         (   0  !>;   0  ?*;   0  @-;   1  @+)

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

thf(v_evs4_decl,type,
    v_evs4: $i ).

thf(c_Yahalom_Oyahalom_decl,type,
    c_Yahalom_Oyahalom: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_NB_decl,type,
    v_NB: $i ).

thf(v_X_decl,type,
    v_X: $i ).

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Osemiring__0_decl,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

thf(tc_IntDef_Oint_decl,type,
    tc_IntDef_Oint: $i ).

thf(c_Divides_Oop_Advd_decl,type,
    c_Divides_Oop_Advd: $i > $i > $i > $o ).

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

thf(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_SetInterval_OatLeast_decl,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
    class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).

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

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

thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

thf(class_Ring__and__Field_Osemiring__1__cancel_decl,type,
    class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).

thf(class_Ring__and__Field_Opordered__semiring_decl,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(class_OrderedGroup_Osemigroup__add_decl,type,
    class_OrderedGroup_Osemigroup__add: $i > $o ).

thf(class_OrderedGroup_Omonoid__mult_decl,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_OrderedGroup_Osemigroup__mult_decl,type,
    class_OrderedGroup_Osemigroup__mult: $i > $o ).

thf(class_Ring__and__Field_Opordered__cancel__comm__semiring_decl,type,
    class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

thf(class_Power_Orecpower_decl,type,
    class_Power_Orecpower: $i > $o ).

thf(class_Orderings_Oord_decl,type,
    class_Orderings_Oord: $i > $o ).

thf(class_HOL_Otimes_decl,type,
    class_HOL_Otimes: $i > $o ).

thf(class_HOL_Ozero_decl,type,
    class_HOL_Ozero: $i > $o ).

thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(class_HOL_Oone_decl,type,
    class_HOL_Oone: $i > $o ).

thf(class_LOrder_Omeet__semilorder_decl,type,
    class_LOrder_Omeet__semilorder: $i > $o ).

thf(class_LOrder_Olorder_decl,type,
    class_LOrder_Olorder: $i > $o ).

thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

thf(class_Ring__and__Field_Osemiring_decl,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

thf(class_Ring__and__Field_Oordered__semidom_decl,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

thf(class_LOrder_Ojoin__semilorder_decl,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

thf(class_Orderings_Oorder_decl,type,
    class_Orderings_Oorder: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

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

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

thf(class_Numeral_Onumber_decl,type,
    class_Numeral_Onumber: $i > $o ).

thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

thf(class_Divides_Odiv_decl,type,
    class_Divides_Odiv: $i > $o ).

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(class_Ring__and__Field_Ocomm__semiring__0__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

thf(class_Parity_Oeven__odd_decl,type,
    class_Parity_Oeven__odd: $i > $o ).

thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

thf(class_Nat_Opower_decl,type,
    class_Nat_Opower: $i > $o ).

thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

thf(c_SetInterval_OgreaterThan_decl,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

thf(class_HOL_Ominus_decl,type,
    class_HOL_Ominus: $i > $o ).

thf(class_Ring__and__Field_Osemiring__1_decl,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

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

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

thf(c_times_decl,type,
    c_times: $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_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_GCD_Ogcd_decl,type,
    c_GCD_Ogcd: $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(c_Suc_decl,type,
    c_Suc: $i > $i ).

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

thf(c_Message_Omsg_OHash_decl,type,
    c_Message_Omsg_OHash: $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_1_decl,type,
    c_1: $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_List_Oremdups_decl,type,
    c_List_Oremdups: $i > $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_UNIV_decl,type,
    c_UNIV: $i ).

thf(c_plus_decl,type,
    c_plus: $i > $i > $i > $i ).

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

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

thf(c_Main_Ozmod__eq__0D__dest__1_decl,type,
    c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).

thf(c_Relation_Otrans_decl,type,
    c_Relation_Otrans: $i > $i > $o ).

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

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

thf(tc_fun_decl,type,
    tc_fun: $i > $i > $i ).

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

thf(c_Message_Osynth_decl,type,
    c_Message_Osynth: $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_Event_Obad_decl,type,
    c_Event_Obad: $i ).

thf(tc_Message_Oagent_decl,type,
    tc_Message_Oagent: $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_Event_Oused_decl,type,
    c_Event_Oused: $i > $i ).

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

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

thf(c_Wellfounded__Relations_Oless__than_decl,type,
    c_Wellfounded__Relations_Oless__than: $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_Infinite__Set_Oatmost__one_decl,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

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_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(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_Omod__eq__0D__dest__1_decl,type,
    c_Main_Omod__eq__0D__dest__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__wPE_decl,type,
    v_sko__wPE: $i > $i > $i > $i ).

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

thf(c_List_Olenlex_decl,type,
    c_List_Olenlex: $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 ).

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

thf(611,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(2163,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

thf(1501,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(582,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(2094,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)],[582]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

thf(1823,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(368,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(1633,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)],[368]) ).

thf(534,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

thf(1995,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(122,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).

thf(1105,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).

thf(1237,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(8,negated_conjecture,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(906,plain,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(909,plain,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[906]) ).

thf(755,axiom,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

thf(2463,plain,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(28,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(941,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(207,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(1294,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(1295,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(polarity_switch,[status(thm)],[1294]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

thf(1322,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(384,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

thf(1665,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(88,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(1036,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(833,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(2630,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)],[833]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

thf(1879,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

thf(1337,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

thf(1024,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(288,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

thf(1469,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(1168,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(672,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

thf(2295,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(678,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(2306,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)],[678]) ).

thf(697,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(2341,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(570,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

thf(2072,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

thf(1767,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

thf(1315,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(816,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(2595,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(739,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(2427,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)],[739]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

thf(1083,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(46,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(962,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

thf(1179,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(693,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(2331,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)],[693]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

thf(1956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(1950,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(667,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(2280,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)],[667]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

thf(1554,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

thf(1686,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(652,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(2248,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(2249,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(polarity_switch,[status(thm)],[2248]) ).

thf(2250,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(lifteq,[status(thm)],[2249]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

thf(1200,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(56,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(977,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)],[56]) ).

thf(169,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(1211,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(591,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

thf(2117,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

thf(1290,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(644,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(2231,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)],[644]) ).

thf(813,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(2590,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)],[813]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

thf(1073,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

thf(1728,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(348,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

thf(1591,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).

thf(1269,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(272,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

thf(1437,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(680,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(2309,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)],[680]) ).

thf(781,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(2512,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)],[781]) ).

thf(772,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(2495,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(923,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(924,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(cnf,[status(esa)],[923]) ).

thf(925,plain,
    ! [A: $i] :
      ( ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
      | ( A = c_0 ) ),
    inference(lifteq,[status(thm)],[924]) ).

thf(6,negated_conjecture,
    tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(901,plain,
    tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(681,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(2311,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(2312,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[2311]) ).

thf(2842,plain,
    ! [A: $i] :
      ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[901,2312]) ).

thf(2843,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2842]) ).

thf(2851,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Message_Omsg )
      | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( v_X != A ) ),
    inference(simp,[status(thm)],[2843]) ).

thf(2856,plain,
    ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
   != ( c_emptyset @ c_Message_Oparts ) ),
    inference(simp,[status(thm)],[2851]) ).

thf(2858,plain,
    ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
   != c_emptyset ),
    inference(simp,[status(thm)],[2856]) ).

thf(3229,plain,
    ! [A: $i] :
      ( ( A
       != ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
      | ( c_emptyset != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[925,2858]) ).

thf(3230,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_IntDef_Oint @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3229:[bind(A,$thf( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ))]]) ).

thf(724,axiom,
    tc_nat @ class_Wellfounded__Recursion_Owellorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).

thf(2395,plain,
    tc_nat @ class_Wellfounded__Recursion_Owellorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(2062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(1443,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(450,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(1808,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)],[450]) ).

thf(850,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(2659,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)],[850]) ).

thf(64,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(994,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(788,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(2527,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)],[788]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

thf(1569,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

thf(1544,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(543,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

thf(2014,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(4,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_X @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Event_Oevent_OGets ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(907,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_X @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Event_Oevent_OGets ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2844,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_X @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Event_Oevent_OGets ) @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[907,2312]) ).

thf(2845,plain,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_X @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Event_Oevent_OGets ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2844]) ).

thf(2849,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_Event_Oevent )
      | ( ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) )
       != ( c_emptyset @ c_Message_Oparts ) )
      | ( ( v_X @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Event_Oevent_OGets ) )
       != A ) ),
    inference(simp,[status(thm)],[2845]) ).

thf(2854,plain,
    ( ( tc_Message_Omsg != tc_Event_Oevent )
    | ( ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) )
     != ( c_emptyset @ c_Message_Oparts ) ) ),
    inference(simp,[status(thm)],[2849]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

thf(1533,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

thf(1497,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(387,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(1671,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)],[387]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

thf(1608,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(136,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1137,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(865,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(2686,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)],[865]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

thf(1735,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

thf(2184,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

thf(1872,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

thf(1233,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

thf(1988,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(32,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(945,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(557,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(2042,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

thf(2146,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(427,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(1756,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(215,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

thf(1310,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

thf(1164,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(536,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(1999,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)],[536]) ).

thf(684,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(2316,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)],[684]) ).

thf(428,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).

thf(1761,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(10,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(913,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(101,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(1063,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)],[101]) ).

thf(514,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

thf(1954,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

thf(1507,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(21,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(930,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(709,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(2360,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)],[709]) ).

thf(117,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(1095,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)],[117]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(1835,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(638,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(2216,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)],[638]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

thf(2046,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(274,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

thf(1441,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(93,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(1046,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)],[93]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

thf(1645,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(575,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(2082,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

thf(2173,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(318,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

thf(1529,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

thf(1803,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(728,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(2405,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)],[728]) ).

thf(482,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

thf(1887,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(701,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(2348,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)],[701]) ).

thf(885,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(2723,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)],[885]) ).

thf(741,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(2432,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(769,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(2491,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)],[769]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

thf(1127,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(797,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(2548,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)],[797]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

thf(1601,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(249,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(1386,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)],[249]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(1724,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

thf(1475,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(2136,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).

thf(1265,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(363,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

thf(1623,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

thf(1254,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(847,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__wPE ) ) @ 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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__Says_0) ).

thf(2654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__wPE ) ) @ 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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(204,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(1287,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)],[204]) ).

thf(820,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(2603,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)],[820]) ).

thf(696,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(2339,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(662,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(2269,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(768,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(2488,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)],[768]) ).

thf(594,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(2126,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(705,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(2356,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)],[705]) ).

thf(875,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(2703,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)],[875]) ).

thf(381,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(1660,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

thf(1298,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(492,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).

thf(1907,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(775,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(2501,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)],[775]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

thf(1330,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(470,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

thf(1860,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

thf(1511,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(664,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(2273,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(2274,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[2273]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(cnf,[status(esa)],[915]) ).

thf(917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Orderings_Olinorder )
      | ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) ) ),
    inference(lifteq,[status(thm)],[916]) ).

thf(863,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(2682,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)],[863]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(1826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(341,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(1577,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)],[341]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

thf(1455,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(25,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(934,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

thf(1191,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(532,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

thf(1992,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(11,axiom,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(914,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(2890,plain,
    ! [A: $i] :
      ( ( A != c_Event_Obad )
      | ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[925,2274]) ).

thf(2891,plain,
    ( ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) )
    | ~ ( tc_IntDef_Oint @ ( c_Event_Obad @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2890:[bind(A,$thf( c_Event_Obad ))]]) ).

thf(3343,plain,
    ( ( ( tc_IntDef_Oint @ ( c_Event_Obad @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[914,2891]) ).

thf(3344,plain,
    ( ( ( tc_IntDef_Oint @ ( c_Event_Obad @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[3343]) ).

thf(3352,plain,
    ( ( tc_IntDef_Oint != tc_IntDef_Oint )
    | ( c_Event_Obad != c_0 )
    | ( c_0 != c_0 )
    | ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[3344]) ).

thf(3353,plain,
    ( ( c_Event_Obad != c_0 )
    | ~ ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[3352]) ).

thf(735,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(2420,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)],[735]) ).

thf(880,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(2713,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)],[880]) ).

thf(484,axiom,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(1892,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(142,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).

thf(1147,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(800,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(2552,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)],[800]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

thf(1704,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(610,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(2158,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)],[610]) ).

thf(372,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(1641,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)],[372]) ).

thf(436,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(1778,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)],[436]) ).

thf(790,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( D @ c_Message_Omsg_OKey @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OA__trusts__YM3_0) ).

thf(2533,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( D @ c_Message_Omsg_OKey @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(465,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(1847,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)],[465]) ).

thf(3,negated_conjecture,
    tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(905,plain,
    tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(2817,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,909]) ).

thf(2818,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
   != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2817]) ).

thf(2829,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
     != c_Message_OsymKeys )
    | ( ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) )
     != v_K ) ),
    inference(simp,[status(thm)],[2818]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).

thf(1922,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(868,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(2691,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)],[868]) ).

thf(9,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).

thf(902,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(614,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

thf(2169,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

thf(1087,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(51,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(969,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(715,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(2373,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)],[715]) ).

thf(232,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

thf(1347,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(420,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(1741,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)],[420]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

thf(1398,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(784,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(2520,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)],[784]) ).

thf(889,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(2730,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)],[889]) ).

thf(675,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(2301,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)],[675]) ).

thf(453,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(1815,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)],[453]) ).

thf(301,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(1494,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)],[301]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).

thf(2007,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(641,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(2222,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(647,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(2237,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)],[647]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).

thf(1302,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

thf(2105,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(657,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(2259,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)],[657]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

thf(1682,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).

thf(1828,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

thf(1151,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(553,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

thf(2034,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

thf(1960,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

thf(1051,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

thf(1946,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

thf(1465,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(688,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( 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__spies_0) ).

thf(2324,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( 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)],[688]) ).

thf(550,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(2027,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)],[550]) ).

thf(494,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(1911,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)],[494]) ).

thf(1,negated_conjecture,
    tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(900,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2770,plain,
    ( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[900,2274]) ).

thf(2771,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2770]) ).

thf(2782,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Oagent )
    | ( c_Event_Obad != c_Yahalom_Oyahalom )
    | ( c_Message_Oagent_OServer != v_evs4 ) ),
    inference(simp,[status(thm)],[2771]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).

thf(1858,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(472,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(1864,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)],[472]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

thf(1020,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(655,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(2254,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)],[655]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

thf(1183,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(202,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(1283,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)],[202]) ).

thf(545,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

thf(2017,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(779,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(2508,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

thf(2058,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(826,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(2618,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)],[826]) ).

thf(171,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(1215,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)],[171]) ).

thf(624,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

thf(2190,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(789,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(2530,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(737,axiom,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(2424,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

thf(1394,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

thf(1351,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(68,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(998,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)],[68]) ).

thf(270,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(1433,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

thf(1405,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(399,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(1697,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(632,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

thf(2205,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(7,negated_conjecture,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(904,plain,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(910,plain,
    ~ ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[904]) ).

thf(2756,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[900,910]) ).

thf(2757,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2756]) ).

thf(2762,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Omsg )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
     != c_Yahalom_Oyahalom )
    | ( ( v_NB @ c_Message_Omsg_ONonce )
     != v_evs4 ) ),
    inference(simp,[status(thm)],[2757]) ).

thf(713,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(2367,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)],[713]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(1928,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(277,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(1447,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)],[277]) ).

thf(40,axiom,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(956,plain,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(1343,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(1344,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(polarity_switch,[status(thm)],[1343]) ).

thf(1345,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(lifteq,[status(thm)],[1344]) ).

thf(838,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(2639,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)],[838]) ).

thf(723,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(2392,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)],[723]) ).

thf(608,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

thf(2154,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

thf(1521,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(376,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(1649,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(1650,plain,
    c_UNIV != c_emptyset,
    inference(polarity_switch,[status(thm)],[1649]) ).

thf(1651,plain,
    c_UNIV != c_emptyset,
    inference(lifteq,[status(thm)],[1650]) ).

thf(355,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(1604,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)],[355]) ).

thf(15,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(920,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)],[15]) ).

thf(29,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(942,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(3298,plain,
    ( ( ( tc_IntDef_Oint @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_emptyset != c_0 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[914,3230]) ).

thf(3299,plain,
    ( ( ( tc_IntDef_Oint @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3298]) ).

thf(3300,plain,
    ( ( tc_IntDef_Oint != tc_IntDef_Oint )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
     != c_0 )
    | ( c_0 != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3299]) ).

thf(3301,plain,
    ( ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
     != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3300]) ).

thf(396,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

thf(1691,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

thf(1306,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(711,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(2364,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)],[711]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

thf(1153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

thf(1783,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

thf(1730,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(842,axiom,
    tc_nat @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(2646,plain,
    tc_nat @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

thf(1708,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(581,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(2093,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(673,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OCrypt__Spy__analz__bad_0) ).

thf(2296,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(679,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(2307,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)],[679]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(1067,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(773,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(2496,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)],[773]) ).

thf(828,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(2621,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(851,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(2660,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)],[851]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

thf(1868,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(719,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(2382,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)],[719]) ).

thf(857,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(2673,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

thf(1091,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(819,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(2601,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)],[819]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

thf(1519,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

thf(1123,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

thf(1217,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(425,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(1751,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)],[425]) ).

thf(821,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(2606,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)],[821]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

thf(2032,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

thf(2132,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(725,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(2396,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)],[725]) ).

thf(876,axiom,
    tc_nat @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(2705,plain,
    tc_nat @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(659,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(2264,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(488,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(1900,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(41,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(957,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

thf(1223,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(890,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(2733,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)],[890]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

thf(1042,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(36,axiom,
    tc_IntDef_Oint @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(952,plain,
    tc_IntDef_Oint @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

thf(1580,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(666,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(2277,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)],[666]) ).

thf(154,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(1174,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)],[154]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

thf(1676,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

thf(1619,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

thf(2150,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(480,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

thf(1883,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

thf(1560,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

thf(1423,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(498,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(1920,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)],[498]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

thf(1968,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(208,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(1296,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

thf(1457,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(629,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(2200,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)],[629]) ).

thf(619,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(2179,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)],[619]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

thf(1787,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

thf(1656,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

thf(1392,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(589,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(2112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).

thf(1012,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(846,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(2653,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(756,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(2464,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)],[756]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).

thf(1938,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(1032,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

thf(1837,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(831,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(2628,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(856,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).

thf(2670,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(742,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(2433,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)],[742]) ).

thf(763,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(2477,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)],[763]) ).

thf(852,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2663,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(694,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(2332,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)],[694]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(1079,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(690,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(2327,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)],[690]) ).

thf(636,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

thf(2213,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(163,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(1195,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)],[163]) ).

thf(635,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(2211,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(259,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(1407,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)],[259]) ).

thf(699,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(2344,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)],[699]) ).

thf(682,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(2313,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)],[682]) ).

thf(200,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(1281,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(893,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(2741,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(339,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(1573,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)],[339]) ).

thf(54,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(974,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(257,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(1402,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)],[257]) ).

thf(527,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(1983,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)],[527]) ).

thf(585,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

thf(2100,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(717,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(2377,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)],[717]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

thf(1328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(708,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(2359,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)],[708]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

thf(1856,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

thf(1587,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(1425,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(71,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(1006,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(887,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(2726,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)],[887]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

thf(1118,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(238,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(1360,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(650,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(2245,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)],[650]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

thf(1936,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(324,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(1541,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)],[324]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

thf(1089,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(774,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( I = C )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_1) ).

thf(2498,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( I = C )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(140,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(1143,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)],[140]) ).

thf(590,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

thf(2115,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

thf(1772,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

thf(1259,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(878,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(2709,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)],[878]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

thf(1970,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(1227,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(137,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(1138,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)],[137]) ).

thf(792,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(2537,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

thf(1567,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(753,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(2460,plain,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

thf(1160,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(803,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(2561,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)],[803]) ).

thf(2819,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
     != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[901,909]) ).

thf(2820,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
   != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2819]) ).

thf(2826,plain,
    ( ( tc_Message_Omsg != tc_Message_Omsg )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
     != ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts ) )
    | ( ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) )
     != v_X ) ),
    inference(simp,[status(thm)],[2820]) ).

thf(2830,plain,
    ( ( v_NB @ c_Message_Omsg_ONonce @ ( v_K @ c_Message_Omsg_OCrypt ) )
   != v_X ),
    inference(simp,[status(thm)],[2826]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).

thf(2080,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(344,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(1584,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

thf(2038,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(854,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(2666,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)],[854]) ).

thf(483,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(1889,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)],[483]) ).

thf(146,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(1155,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)],[146]) ).

thf(84,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(1028,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)],[84]) ).

thf(548,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(2023,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)],[548]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

thf(1964,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

thf(1942,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(206,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

thf(1292,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(24,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(933,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(1739,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

thf(1461,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(734,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(2419,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)],[734]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(1075,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(752,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(2455,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)],[752]) ).

thf(261,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(1414,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

thf(2196,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(401,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

thf(1700,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(824,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(2613,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)],[824]) ).

thf(451,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(1810,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)],[451]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

thf(1791,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(799,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(2551,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)],[799]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

thf(1016,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(167,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(1207,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)],[167]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

thf(2085,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

thf(1612,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(761,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(2472,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)],[761]) ).

thf(844,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(2649,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)],[844]) ).

thf(90,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(1039,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)],[90]) ).

thf(52,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(970,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(2774,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[901,2274]) ).

thf(2775,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2774]) ).

thf(2781,plain,
    ( ( tc_Message_Oagent != tc_Message_Omsg )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
     != c_Event_Obad )
    | ( v_X != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[2775]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).

thf(1419,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

thf(1451,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(767,axiom,
    tc_nat @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(2487,plain,
    tc_nat @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

thf(1231,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).

thf(1131,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(524,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(1974,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)],[524]) ).

thf(329,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

thf(1552,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(704,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(2355,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(1984,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

thf(1852,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(477,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(1874,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)],[477]) ).

thf(268,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(1429,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)],[268]) ).

thf(408,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(1715,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)],[408]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

thf(1720,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(525,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

thf(1979,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(601,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(2140,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)],[601]) ).

thf(457,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(1825,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(1114,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

thf(1324,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(668,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(2285,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)],[668]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).

thf(1776,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

thf(1263,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(67,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(997,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(751,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(2450,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)],[751]) ).

thf(119,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(1099,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)],[119]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

thf(1478,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(188,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(1249,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)],[188]) ).

thf(783,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

thf(2519,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

thf(1539,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

thf(1382,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(757,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(2465,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)],[757]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(1060,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(59,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(984,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)],[59]) ).

thf(777,axiom,
    tc_nat @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(2505,plain,
    tc_nat @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(805,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(2566,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)],[805]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(1799,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(562,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(2052,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

thf(1599,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(871,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(2697,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)],[871]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

thf(1246,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

thf(1627,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(714,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( K = F )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_3) ).

thf(2370,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( K = F )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

thf(1525,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(27,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(936,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)],[27]) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(cnf,[status(esa)],[936]) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(lifteq,[status(thm)],[937]) ).

thf(398,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).

thf(1695,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(1054,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(1515,plain,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(736,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(2423,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(416,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(1732,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)],[416]) ).

thf(17,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(926,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(835,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(2634,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)],[835]) ).

thf(897,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(2749,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)],[897]) ).

thf(165,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

thf(1202,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).

thf(2203,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(184,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(1241,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)],[184]) ).

thf(874,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(2702,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(796,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(2546,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)],[796]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

thf(2076,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

thf(1170,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

thf(1071,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(727,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(2402,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)],[727]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

thf(1187,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(746,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(2440,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)],[746]) ).

thf(729,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(2408,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)],[729]) ).

thf(2340,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[2339]) ).

thf(2789,plain,
    ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
     != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[901,2340]) ).

thf(2790,plain,
    ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
   != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2789]) ).

thf(2793,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_Message_Omsg )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
     != c_Finite__Set_OFinites )
    | ( c_UNIV != v_X ) ),
    inference(simp,[status(thm)],[2790]) ).

thf(383,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(1663,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)],[383]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

thf(2089,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

thf(1026,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(486,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(1895,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)],[486]) ).

thf(37,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(953,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1185,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

thf(1135,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(537,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(2001,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(731,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(2413,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)],[731]) ).

thf(860,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(2677,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)],[860]) ).

thf(391,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

thf(1680,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(665,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(2275,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)],[665]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

thf(1483,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(807,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(2570,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)],[807]) ).

thf(327,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(1548,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)],[327]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(1631,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(593,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(2121,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)],[593]) ).

thf(646,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(2235,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)],[646]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).

thf(2144,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

thf(1754,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(670,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(2292,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)],[670]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(1698,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(802,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(2556,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)],[802]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

thf(1103,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(882,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(2717,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)],[882]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

thf(1219,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(3354,plain,
    ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
    | ( c_Event_Obad != c_0 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,3353]) ).

thf(3355,plain,
    ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_0 @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
    | ( c_Event_Obad != c_0 ) ),
    inference(simp,[status(thm)],[3354]) ).

thf(3375,plain,
    ( ( tc_Message_Oagent != tc_nat )
    | ( c_0 != c_Message_OsymKeys )
    | ( v_K != c_Message_Oagent_OServer )
    | ( c_Event_Obad != c_0 ) ),
    inference(simp,[status(thm)],[3355]) ).

thf(350,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(1595,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(72,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(1007,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

thf(1916,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(642,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(2225,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)],[642]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

thf(1125,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(623,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

thf(2188,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

thf(1652,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(250,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(1388,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)],[250]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

thf(1535,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(42,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(958,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

thf(1795,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

thf(2134,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(55,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(975,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

thf(2048,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(2937,plain,
    ! [A: $i] :
      ( ( A != c_UNIV )
      | ( c_emptyset != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[925,1651]) ).

thf(2938,plain,
    ( ( c_emptyset != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[2937:[bind(A,$thf( c_UNIV ))]]) ).

thf(786,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(2525,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(849,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(2657,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)],[849]) ).

thf(858,axiom,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(2674,plain,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(544,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(2016,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(782,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(2514,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)],[782]) ).

thf(806,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(2568,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)],[806]) ).

thf(191,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(1256,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)],[191]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

thf(1488,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(305,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

thf(1503,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(1669,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(640,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(2220,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)],[640]) ).

thf(689,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(2326,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(216,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(1312,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)],[216]) ).

thf(892,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(2738,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)],[892]) ).

thf(369,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

thf(1635,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(225,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(1332,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)],[225]) ).

thf(877,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(2706,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)],[877]) ).

thf(3302,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
       != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[925,3301]) ).

thf(3303,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
       != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[3302]) ).

thf(3304,plain,
    ( ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
     != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3303:[bind(A,$thf( c_emptyset ))]]) ).

thf(33,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(947,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)],[33]) ).

thf(198,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(1271,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)],[198]) ).

thf(98,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(1058,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(123,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(1107,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)],[123]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

thf(1239,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(1997,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(612,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(2166,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

thf(1765,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(487,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(1897,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)],[487]) ).

thf(14,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(919,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(707,axiom,
    tc_nat @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(2358,plain,
    tc_nat @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

thf(1356,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(808,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( J = E )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_2) ).

thf(2573,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( J = E )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

thf(2148,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(780,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(2510,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)],[780]) ).

thf(700,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(2346,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)],[700]) ).

thf(793,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(2538,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)],[793]) ).

thf(201,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1282,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(840,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(2642,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)],[840]) ).

thf(576,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(2084,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(837,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(2637,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)],[837]) ).

thf(75,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(1011,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

thf(1349,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

thf(1722,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(1801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).

thf(1209,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(592,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(2119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(861,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(2679,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(732,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(2415,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)],[732]) ).

thf(770,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(2493,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)],[770]) ).

thf(66,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(996,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(504,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(1933,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)],[504]) ).

thf(656,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(2257,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)],[656]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

thf(1589,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(651,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(2246,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)],[651]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

thf(1492,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(354,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(1603,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)],[354]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(244,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

thf(1376,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

thf(1439,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

thf(1667,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

thf(2182,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

thf(1471,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(698,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(2343,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

thf(1993,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

thf(1821,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(748,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(2446,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(1862,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(814,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(2593,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(754,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(2461,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)],[754]) ).

thf(454,axiom,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(1820,plain,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

thf(2025,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(834,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(2632,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(2768,plain,
    ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
     != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,2274]) ).

thf(2769,plain,
    ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
   != ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2768]) ).

thf(2780,plain,
    ( ( tc_Message_Oagent != tc_nat )
    | ( c_Event_Obad != c_Message_OsymKeys )
    | ( v_K != c_Message_Oagent_OServer ) ),
    inference(simp,[status(thm)],[2769]) ).

thf(661,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(2267,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)],[661]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(1909,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(148,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

thf(1162,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(48,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(964,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)],[48]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

thf(1556,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(843,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(2647,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)],[843]) ).

thf(30,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(943,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).

thf(1022,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(654,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(2252,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)],[654]) ).

thf(853,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(2664,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)],[853]) ).

thf(691,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(2329,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)],[691]) ).

thf(23,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(932,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(513,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).

thf(1112,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(395,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(1688,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)],[395]) ).

thf(2,negated_conjecture,
    v_A != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(903,plain,
    v_A != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(911,plain,
    v_A != c_Message_Oagent_OServer,
    inference(polarity_switch,[status(thm)],[903]) ).

thf(912,plain,
    c_Message_Oagent_OServer != v_A,
    inference(lifteq,[status(thm)],[911]) ).

thf(58,axiom,
    tc_IntDef_Oint @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(983,plain,
    tc_IntDef_Oint @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

thf(1926,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(702,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(2350,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)],[702]) ).

thf(886,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(2725,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

thf(1213,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

thf(1445,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

thf(1643,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(568,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(2064,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)],[568]) ).

thf(60,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(986,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)],[60]) ).

thf(2785,plain,
    ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
     != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[900,2340]) ).

thf(2786,plain,
    ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
   != ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2785]) ).

thf(2797,plain,
    ( ( ( tc_nat @ tc_set )
     != ( tc_Event_Oevent @ tc_List_Olist ) )
    | ( c_Finite__Set_OFinites != c_Yahalom_Oyahalom )
    | ( c_UNIV != v_evs4 ) ),
    inference(simp,[status(thm)],[2786]) ).

thf(939,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[938]) ).

thf(940,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Orev ) @ ( B @ sk1 ) )
      = A ),
    inference(cnf,[status(esa)],[939]) ).

thf(3310,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Orev ) @ ( B @ sk1 ) )
      = A ),
    inference(lifteq,[status(thm)],[940]) ).

thf(292,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(791,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(2535,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)],[791]) ).

thf(676,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(2303,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)],[676]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(2156,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(633,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

thf(2207,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(449,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(1805,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)],[449]) ).

thf(569,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(2069,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)],[569]) ).

thf(254,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(1396,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(745,axiom,
    tc_nat @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(2439,plain,
    tc_nat @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(43,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(959,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(615,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

thf(2171,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

thf(1044,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(798,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(2550,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(649,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(2244,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(69,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(1000,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)],[69]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

thf(1435,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(413,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(1726,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)],[413]) ).

thf(240,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(1364,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)],[240]) ).

thf(722,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(2390,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)],[722]) ).

thf(921,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    inference(cnf,[status(esa)],[920]) ).

thf(922,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    inference(lifteq,[status(thm)],[921]) ).

thf(869,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(2693,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)],[869]) ).

thf(778,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(2506,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)],[778]) ).

thf(334,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(2005,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

thf(2096,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

thf(1304,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(31,axiom,
    tc_IntDef_Oint @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(944,plain,
    tc_IntDef_Oint @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(287,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(1467,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(491,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(1905,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)],[491]) ).

thf(18,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(927,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(645,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(2234,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)],[645]) ).

thf(811,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(2582,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)],[811]) ).

thf(563,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

thf(2054,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(1948,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

thf(1034,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(648,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(2239,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)],[648]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

thf(1166,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(588,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(2107,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)],[588]) ).

thf(685,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).

thf(2318,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(663,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(2271,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)],[663]) ).

thf(845,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(2652,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(760,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(2471,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(776,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(2503,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)],[776]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).

thf(1684,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(750,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(2449,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

thf(1509,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

thf(1081,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(832,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(2629,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)],[832]) ).

thf(531,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(864,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(2684,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)],[864]) ).

thf(630,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(2202,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(1145,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

thf(1018,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(817,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(2597,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)],[817]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

thf(1958,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(50,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(968,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).

thf(1181,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(423,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(1748,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(674,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(2298,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(881,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(2715,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)],[881]) ).

thf(716,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ 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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).

thf(2375,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ 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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(2192,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(53,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(971,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)],[53]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

thf(2012,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(375,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

thf(1647,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(617,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).

thf(2175,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

thf(1267,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(884,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( H = B )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_0) ).

thf(2720,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( H = B )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(1531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(63,axiom,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(993,plain,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

thf(1225,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(566,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(2060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

thf(1743,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

thf(1400,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(38,axiom,
    tc_IntDef_Oint @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(954,plain,
    tc_IntDef_Oint @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(3243,plain,
    ( ( ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_emptyset != c_0 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[914,2938]) ).

thf(3244,plain,
    ( ( ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) )
     != ( tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3243]) ).

thf(3245,plain,
    ( ( tc_IntDef_Oint != tc_IntDef_Oint )
    | ( c_UNIV != c_0 )
    | ( c_0 != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3244]) ).

thf(3246,plain,
    ( ( c_UNIV != c_0 )
    | ( c_emptyset != c_0 ) ),
    inference(simp,[status(thm)],[3245]) ).

thf(2223,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(polarity_switch,[status(thm)],[2222]) ).

thf(2224,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(lifteq,[status(thm)],[2223]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).

thf(1785,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

thf(1235,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(695,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(2337,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)],[695]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

thf(2128,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

thf(1901,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(558,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(2044,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(1285,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(848,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(2656,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)],[848]) ).

thf(896,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(2747,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)],[896]) ).

thf(95,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

thf(1053,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).

thf(1499,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(1813,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

thf(1300,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

thf(1637,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(866,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(2688,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)],[866]) ).

thf(218,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(1317,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)],[218]) ).

thf(460,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(1830,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)],[460]) ).

thf(429,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(1763,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)],[429]) ).

thf(112,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(1085,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)],[112]) ).

thf(380,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(1658,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)],[380]) ).

thf(687,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(2322,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(873,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(2701,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(35,axiom,
    tc_IntDef_Oint @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(951,plain,
    tc_IntDef_Oint @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(795,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(2545,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(730,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(2411,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(794,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(2543,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)],[794]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

thf(1221,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).

thf(2579,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

thf(1797,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(73,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(1008,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(242,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

thf(1372,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

thf(1881,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(61,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(991,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(859,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(2675,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)],[859]) ).

thf(564,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

thf(2056,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(237,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(1358,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)],[237]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(1141,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(738,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(2426,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).

thf(1981,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

thf(1702,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(718,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(2379,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)],[718]) ).

thf(235,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(1353,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)],[235]) ).

thf(706,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(2357,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(1485,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).

thf(1972,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(2319,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(polarity_switch,[status(thm)],[2318]) ).

thf(2320,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(lifteq,[status(thm)],[2319]) ).

thf(879,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(2711,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)],[879]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(1749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

thf(1427,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

thf(1585,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(138,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(1140,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(888,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(2728,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)],[888]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

thf(2030,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

thf(1940,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(2752,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,910]) ).

thf(2753,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
   != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2752]) ).

thf(2760,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
     != c_Message_OsymKeys )
    | ( ( v_NB @ c_Message_Omsg_ONonce )
     != v_K ) ),
    inference(simp,[status(thm)],[2753]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(1421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(463,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(1839,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)],[463]) ).

thf(764,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(2479,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)],[764]) ).

thf(283,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).

thf(1459,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

thf(1966,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(22,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(931,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(870,axiom,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(2696,plain,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

thf(2078,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(626,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(2194,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(823,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(2611,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)],[823]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

thf(1866,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(830,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(2626,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(497,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(1918,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)],[497]) ).

thf(703,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(2352,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)],[703]) ).

thf(464,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(1844,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)],[464]) ).

thf(378,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(1654,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(260,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

thf(1412,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(637,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(2215,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(1517,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

thf(1781,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(634,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(2209,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(894,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(2743,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)],[894]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(1189,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).

thf(1390,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(677,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(2305,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

thf(1575,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(280,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

thf(1453,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(841,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(2643,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)],[841]) ).

thf(199,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(1276,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)],[199]) ).

thf(747,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(2443,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)],[747]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

thf(1326,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(721,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(2389,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)],[721]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

thf(1903,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(801,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(2554,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)],[801]) ).

thf(100,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(1062,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(1481,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(1629,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(422,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(1745,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)],[422]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

thf(1854,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(822,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(2608,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)],[822]) ).

thf(787,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(2526,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)],[787]) ).

thf(45,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(961,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(815,axiom,
    tc_nat @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(2594,plain,
    tc_nat @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(47,axiom,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(963,plain,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(2167,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

thf(1341,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

thf(2098,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

thf(1674,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(2838,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[900,2312]) ).

thf(2839,plain,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs4 @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2838]) ).

thf(2850,plain,
    ! [A: $i] :
      ( ( ( tc_Event_Oevent @ tc_List_Olist )
       != tc_Message_Omsg )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Yahalom_Oyahalom )
      | ( v_evs4 != A ) ),
    inference(simp,[status(thm)],[2839]) ).

thf(2855,plain,
    ( ( ( tc_Event_Oevent @ tc_List_Olist )
     != tc_Message_Omsg )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Yahalom_Oyahalom ) ),
    inference(simp,[status(thm)],[2850]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

thf(1639,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(2840,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
       != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,2312]) ).

thf(2841,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
     != ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2840]) ).

thf(2848,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg != tc_nat )
      | ( ( c_emptyset @ c_Message_Oparts )
       != c_Message_OsymKeys )
      | ( v_K != A ) ),
    inference(simp,[status(thm)],[2841]) ).

thf(2853,plain,
    ( ( tc_Message_Omsg != tc_nat )
    | ( ( c_emptyset @ c_Message_Oparts )
     != c_Message_OsymKeys ) ),
    inference(simp,[status(thm)],[2848]) ).

thf(653,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(2251,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(946,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    inference(lifteq,[status(thm)],[945]) ).

thf(120,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

thf(1101,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(1244,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(2754,plain,
    ( ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
     != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[901,910]) ).

thf(2755,plain,
    ( ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_NB @ c_Message_Omsg_ONonce @ c_in ) ) )
   != ( tc_Message_Omsg @ ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2754]) ).

thf(2761,plain,
    ( ( tc_Message_Omsg != tc_Message_Omsg )
    | ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
     != ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts ) )
    | ( ( v_NB @ c_Message_Omsg_ONonce )
     != v_X ) ),
    inference(simp,[status(thm)],[2755]) ).

thf(2764,plain,
    ( ( ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
     != ( v_evs4 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts ) )
    | ( ( v_NB @ c_Message_Omsg_ONonce )
     != v_X ) ),
    inference(simp,[status(thm)],[2761]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

thf(1523,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

thf(2130,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(65,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(995,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

thf(1558,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).

thf(2152,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(658,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(2262,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)],[658]) ).

thf(749,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(2447,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)],[749]) ).

thf(541,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(2009,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)],[541]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).

thf(1030,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(726,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(2399,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)],[726]) ).

thf(809,axiom,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(2576,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(862,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(2680,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)],[862]) ).

thf(310,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(1513,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)],[310]) ).

thf(683,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).

thf(2315,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(771,axiom,
    tc_nat @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(2494,plain,
    tc_nat @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(829,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(2623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

thf(2019,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(360,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(1614,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)],[360]) ).

thf(720,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(2384,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(762,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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK__D__dest_0) ).

thf(2475,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_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(3265,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_UNIV != c_0 )
      | ( c_0 != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[925,3246]) ).

thf(3266,plain,
    ! [A: $i] :
      ( ( A != c_emptyset )
      | ( c_UNIV != c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(simp,[status(thm)],[3265]) ).

thf(3267,plain,
    ( ( c_UNIV != c_0 )
    | ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(pattern_uni,[status(thm)],[3266:[bind(A,$thf( c_emptyset ))]]) ).

thf(20,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(929,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(692,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(2330,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)],[692]) ).

thf(214,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

thf(1308,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(628,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

thf(2198,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

thf(1706,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(162,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(1193,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)],[162]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

thf(1077,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(710,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(2362,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)],[710]) ).

thf(5,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_NA @ c_Message_Omsg_ONonce @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(899,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_NA @ c_Message_Omsg_ONonce @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

thf(1661,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(643,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(2230,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

thf(2036,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

thf(1893,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(671,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(2294,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)],[671]) ).

thf(669,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(2287,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)],[669]) ).

thf(586,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(2102,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)],[586]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

thf(1678,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

thf(1229,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

thf(1546,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(364,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(1625,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)],[364]) ).

thf(785,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(2522,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)],[785]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

thf(1527,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(294,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(1480,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).

thf(1116,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(538,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(2003,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)],[538]) ).

thf(602,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

thf(2142,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(639,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(2218,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)],[639]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(1133,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(49,axiom,
    tc_IntDef_Oint @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(967,plain,
    tc_IntDef_Oint @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(883,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(2719,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(34,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(950,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

thf(1097,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(812,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(2587,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

thf(1593,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(246,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

thf(1380,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(891,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(2736,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)],[891]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

thf(1986,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(187,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(1248,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

thf(2050,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(836,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(2636,plain,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(898,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(2751,plain,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(13,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(918,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(239,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(1363,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(622,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

thf(2186,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(895,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(2746,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(712,axiom,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(2366,plain,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(406,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(1710,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)],[406]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(2091,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

thf(2040,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(39,axiom,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(955,plain,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(19,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(928,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

thf(1335,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).

thf(1693,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

thf(1172,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(733,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(2417,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)],[733]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

thf(1056,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(1789,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(44,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(960,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(2783,plain,
    ( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
     != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[905,2340]) ).

thf(2784,plain,
    ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
   != ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) ),
    inference(simp,[status(thm)],[2783]) ).

thf(2795,plain,
    ( ( ( tc_nat @ tc_set )
     != tc_nat )
    | ( c_Finite__Set_OFinites != c_Message_OsymKeys )
    | ( c_UNIV != v_K ) ),
    inference(simp,[status(thm)],[2784]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).

thf(1473,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(827,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(2619,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)],[827]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(1065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(855,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(2668,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)],[855]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

thf(2021,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(231,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(1346,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

thf(1610,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).

thf(1129,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

thf(1261,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(740,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(2430,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)],[740]) ).

thf(245,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

thf(1378,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(758,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(2467,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

thf(1550,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

thf(1713,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(128,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(1120,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)],[128]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

thf(2138,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

thf(1093,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(503,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(1930,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(818,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(2600,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).

thf(1384,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(766,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(2485,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)],[766]) ).

thf(322,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

thf(1537,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(343,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

thf(1582,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(660,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(2265,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)],[660]) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs4 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
    inference(polarity_switch,[status(thm)],[902]) ).

thf(62,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(992,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(1597,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(57,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

thf(982,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(1431,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(765,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(2484,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

thf(1885,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(872,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(2699,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)],[872]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

thf(1505,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(362,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(1621,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)],[362]) ).

thf(356,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

thf(1606,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(839,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(2640,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)],[839]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

thf(1320,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(518,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

thf(1962,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(804,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(2563,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)],[804]) ).

thf(571,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(2074,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(743,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(2436,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)],[743]) ).

thf(578,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

thf(2087,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(759,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(2470,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

thf(1069,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(618,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(2177,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)],[618]) ).

thf(686,axiom,
    tc_nat @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(2321,plain,
    tc_nat @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

thf(1944,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(241,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(1367,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)],[241]) ).

thf(26,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(935,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(1009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

thf(1737,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(867,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(2690,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

thf(1463,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(335,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).

thf(1565,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(744,axiom,
    tc_nat @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(2438,plain,
    tc_nat @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

thf(1490,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

thf(1037,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(825,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(2615,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)],[825]) ).

thf(432,axiom,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(1769,plain,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(166,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(1204,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)],[166]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

thf(1449,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(1014,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(262,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(1417,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

thf(1870,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(52581,plain,
    $false,
    inference(e,[status(thm)],[2163,1501,2094,1823,1633,1995,1105,1237,909,2463,941,1295,1322,1665,1036,2630,1879,1337,1718,1024,1469,1168,2295,2306,2341,2072,1767,1315,2595,2427,1083,962,1179,2331,1956,1950,2280,1554,1686,2250,1200,977,1211,1924,2117,1290,2231,2590,1073,1728,1591,1269,1437,2309,2512,2495,3230,2395,2062,1443,1808,2659,994,2527,1569,2248,1544,2014,1793,2854,1533,1497,1671,1608,1137,2686,1735,2184,1872,1233,1988,945,2042,2146,1756,1310,1164,1999,2316,1761,913,1063,1954,1507,930,2360,1095,1835,2216,2046,1441,1046,1645,2082,2173,1529,1803,2405,1887,2348,2723,2432,1914,2491,1127,2548,1601,1386,1724,1475,2136,1265,1623,1254,2654,1287,2603,2339,2269,2488,2126,2356,2703,1660,1298,1907,2501,1330,1860,1511,2274,917,2682,1826,1577,1455,934,1191,1992,3353,2420,2713,1892,1147,2552,1704,2158,1641,1778,2533,1847,2829,1922,2691,902,2169,1087,969,2373,1347,1741,1398,2520,2730,2301,1815,1494,2007,2222,2237,1302,2105,2259,1682,1828,1151,2034,1960,1051,1946,1465,2324,2027,1911,2782,1858,1864,1020,2254,1183,1283,2017,905,2508,2058,2618,1215,2190,2530,2424,1394,1351,998,1433,1405,1697,2205,2762,2367,1928,1447,956,1345,2639,2392,2154,1521,1651,1604,920,942,3301,1691,1306,2364,1153,1783,1730,2646,925,1708,2093,2296,2307,1067,2496,2621,2660,1868,2382,2673,1091,2601,1519,1123,1217,1751,2606,2032,2132,2396,2705,2264,1900,910,957,1223,2733,1343,1042,952,1580,2277,1174,1676,1619,2150,1883,1560,1423,1920,1968,1296,1457,2200,2179,1787,1656,1392,2112,1012,2653,2464,1938,1032,1837,2628,2670,2433,2477,2663,2332,1079,2327,2213,1195,2211,1407,2344,2313,1281,2741,1573,974,1402,1983,2100,2377,1328,2359,1856,1587,1425,1006,2726,1118,1360,2245,1936,1541,1089,2498,1143,2115,1772,1259,2709,1970,1227,1138,2858,2537,1567,2460,1160,2561,2830,2080,1584,2038,2666,1889,1155,1028,2023,1964,1942,1292,933,1739,1461,901,2419,1075,2312,2455,1414,2196,1700,2613,1810,1791,2551,1016,1207,2085,1612,2472,2649,1039,970,2781,1419,1451,2487,1231,1131,1974,1552,2355,1984,1852,1874,1429,1715,1720,1979,2140,1825,1114,1324,2285,1776,1263,997,2450,1099,1478,1249,2519,1539,1382,2465,1060,984,2505,2566,1799,2052,1599,2697,1246,1627,2370,1525,938,1695,1054,1515,2423,1732,926,2634,2749,1202,2203,1241,2702,2546,2076,1170,1071,2402,1187,2440,2408,2793,1663,2089,1026,1895,953,1185,1135,2001,2413,2677,1680,2275,1483,2570,1548,1374,1631,2121,2235,2144,906,1754,2292,1698,2556,1103,2717,1219,3375,1595,1007,1916,2225,1125,2188,1652,1388,1535,958,1795,2134,904,975,2048,2938,2525,2657,2674,2016,2514,2568,1256,1488,1503,1669,936,2220,2326,1312,2738,1635,1332,2706,3304,947,2891,1271,1058,1107,1239,1997,2166,1765,1897,919,2358,1356,2573,2148,2510,2346,2311,2538,1282,2642,2084,2637,1011,1349,1722,1801,2856,1209,2119,900,2679,2415,2493,996,1933,2257,1589,2246,1492,1603,1571,1376,1439,1667,2182,1471,1339,2343,1993,1821,2446,1862,2593,915,2461,1820,2025,2632,2780,2267,1909,1162,1149,964,1556,2647,943,1022,2252,2664,2329,932,1952,1112,1688,912,983,1926,2350,2725,1213,1445,1643,2064,986,2797,3310,1477,2535,2303,2156,2207,1805,2069,1396,2439,959,2171,1044,2550,2244,1000,1435,1726,1364,2390,922,2693,2506,1562,2005,2096,1304,944,1467,1905,927,2234,2582,2054,1948,1034,2239,1166,2107,2318,2271,2652,2471,2503,1684,2449,1509,1081,2629,1990,2684,2202,1145,1018,2597,1958,968,1181,1748,2298,1003,2715,2375,2192,971,2012,1647,2175,1267,2720,1531,993,1225,2060,1743,1400,954,1252,3246,2224,1785,1235,2337,2128,1901,2044,1285,907,2656,2747,1053,1499,1813,1300,1637,2688,1317,1830,1763,1085,1658,2322,2701,951,2545,2411,2543,1221,2579,1797,1008,1372,1881,991,2675,2056,1358,1141,2426,1981,1702,2379,1353,2357,1485,1972,2320,2711,1749,1427,1585,1140,2728,2030,1940,2760,1421,1839,2479,1459,1966,931,2696,2078,2194,2611,1866,2626,1918,1649,2352,1844,903,1654,1412,2215,1517,1781,2209,2743,1189,1390,2305,1575,1453,2643,1276,2443,1326,2389,1903,2554,1062,1481,1629,1745,1854,2608,2526,961,2594,963,2167,2273,1341,2098,1674,2855,1639,2853,2251,946,1101,1244,2764,1523,2130,995,1558,2152,2262,2447,2009,1030,914,2399,2576,2680,1513,2315,2494,2623,2019,1614,2384,2475,3267,1294,929,2330,1308,2198,1706,1193,1077,2362,899,1661,2230,2036,1893,2294,2287,2102,1774,1678,1229,1546,1625,2522,1527,1480,1116,2003,2142,2218,1133,967,2719,950,1097,2587,1593,1380,2736,1986,1248,2050,2636,2751,918,1363,2186,2746,2366,1710,2091,2040,955,928,1335,1693,1172,2417,1056,1789,960,2795,1473,2619,1065,2340,2668,2021,1346,1610,1129,1261,2430,1378,2467,1550,1713,1120,2138,1093,1930,2600,1384,2485,1537,1582,2265,908,992,1597,982,1431,2484,1885,2699,1505,1621,1606,2640,1320,1962,2563,2074,2436,2087,2470,1069,2177,2321,1944,1367,935,1009,923,1737,2690,1463,1565,2438,1490,1037,2615,1769,1204,1449,1014,1417,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWV337-1 : 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
% 0.14/0.39  % Computer : n026.cluster.edu
% 0.14/0.39  % Model    : x86_64 x86_64
% 0.14/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39  % Memory   : 8046.5625MB
% 0.14/0.39  % OS       : Linux 6.8.0-71-generic
% 0.14/0.39  % CPULimit : 300
% 0.14/0.39  % WCLimit  : 300
% 0.14/0.39  % DateTime : Sat Sep 26 13:37:27 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  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
% 0.85/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.31/1.42  % [INFO] 	 Parsing done (434ms). 
% 2.31/1.44  % [INFO] 	 Running in sequential loop mode. 
% 2.77/1.64  % [INFO] 	 eprover registered as external prover. 
% 2.77/1.64  % [INFO] 	 Scanning for conjecture ... 
% 3.02/1.77  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1479 axioms. Running axiom selection ... 
% 3.99/2.02  % [INFO] 	 Axiom selection finished. Selected 889 axioms (removed 590 axioms). 
% 5.39/2.20  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.39/2.22  % [INFO] 	 Type checking passed. 
% 5.39/2.22  % [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 ... 
% 148.81/42.55  % External prover 'e' found a proof!
% 148.81/42.56  % [INFO] 	 Killing All external provers ... 
% 148.81/42.56  % Time passed: 42014ms (effective reasoning time: 41111ms)
% 148.81/42.57  % Axioms used in derivation (889): clsrel_Ring__and__Field_Osemiring__1__cancel_9, cls_Yahalom_OSpy__see__shrK__D__dest_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Osemiring__1__cancel_12, cls_Nat_Ole__0__eq__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, cls_List_Olistrel__Cons1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_14, cls_Message_Omsg_Oinject__7__iff1_0, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, cls_Message_Oanalz_OInj_0, cls_IntDiv_Ozdvd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, clsarity_IntDef__Oint_4, 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_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, cls_Public_Onot__symKeys__pubK__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodI_0, clsrel_Ring__and__Field_Oordered__semidom_16, cls_List_Oappend__in__lists__conv__iff2_0, clsarity_nat_32, clsarity_nat_26, cls_Yahalom_Ounique__session__keys__dest_3, cls_Event_Oevent_Odistinct__3__iff1_0, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Olength__remdups__eq__iff2_0, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, cls_Event_OSays__imp__analz__Spy__dest_0, clsrel_Ring__and__Field_Osemiring__0__cancel_9, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_Public_OpublicKey__into__used_0, clsarity_IntDef__Oint_45, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20, clsrel_Power_Orecpower_17, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7, cls_List_Olistrel__Cons2_1, cls_Public_ONonce__notin__initState__iff1_0, cls_Divides_Omod__eq__0D__dest_0, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_Message_OMPair__eq__HPair__iff1_1, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, cls_List_ONil__is__append__conv__iff2_0, clsrel_Power_Orecpower_14, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_OrderedGroup_Omonoid__mult_2, clsarity_IntDef__Oint_24, clsrel_OrderedGroup_Osemigroup__add_0, cls_Message_Osynth_OAgent_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, clsarity_nat_15, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4, clsrel_Power_Orecpower_21, clsrel_Wellfounded__Recursion_Owellorder_4, cls_Event_Oevent_Odistinct__1__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_12, clsrel_Power_Orecpower_6, clsarity_nat_10, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4, cls_IntDiv_Ozdvd__0__left__iff2_0, cls_Nat_Oless__Suc0__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_List_Orev__eq__Cons__iff__iff2_0, cls_Event_OSays__imp__spies_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, clsrel_Ring__and__Field_Osemiring_1, 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_Finite__Set_OFinites_OemptyI_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, cls_Message_OHPair__neqs__1__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_23, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, cls_Event_Oevent_Oinject__3__iff1_0, clsarity_nat_40, clsrel_Power_Orecpower_5, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, cls_Message_Oagent_Odistinct__5__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, cls_Message_Oagent_Oinject__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsarity_nat_25, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, cls_Message_OHPair__neqs__3__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, cls_Event_Oevent_Oinject__1__iff1_2, clsarity_set_2, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Wellfounded__Recursion_Owellorder_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_List_Olistrel__Nil1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, clsarity_IntDef__Oint_3, cls_Nat_Onot__less0__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Ring__and__Field_Opordered__comm__semiring_8, cls_Public_OshrK_AX_A_58_AsymKeys_0, cls_Finite__Set_Ofinite__Int_0, cls_Nat_Oless__one__iff1_0, cls_Yahalom_OA__trusts__YM3_0, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, cls_Message_OMPair__synth__analz__iff1_1, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, clsrel_Ring__and__Field_Ocomm__semiring__0_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_Message_OHPair__eq__iff1_0, clsarity_nat_47, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsrel_Ring__and__Field_Oordered__semiring__strict_19, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, clsrel_Ring__and__Field_Osemiring__1_4, clsarity_IntDef__Oint_38, cls_Message_OMPair__eq__HPair__iff1_0, clsrel_OrderedGroup_Oab__semigroup__mult_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, clsrel_Ring__and__Field_Opordered__semiring_2, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Yahalom_Ounique__session__keys__dest_0, cls_List_ONil__is__append__conv__iff1_0, clsrel_Wellfounded__Recursion_Owellorder_5, cls_Relation_Orel__compE_0, cls_Message_Oagent_Odistinct__6__iff1_0, cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, cls_Message_Osynth_OHash_0, clsrel_Ring__and__Field_Osemiring__0_2, cls_Message_Omsg_Oinject__7__iff1_1, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Osemiring__0_7, clsarity_nat_36, clsarity_nat_18, cls_Set_OinsertCI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14, clsarity_IntDef__Oint_16, clsrel_Ring__and__Field_Oordered__semiring__strict_3, clsrel_Ring__and__Field_Osemiring__1_10, cls_Relation_ORangeE_0, cls_Message_Osynth_ONumber_0, cls_SetInterval_OlessThan__iff__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_8, cls_Set_OInterI_1, cls_List_Oset__empty__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_16, cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0, cls_Set_OUnCI_1, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, clsrel_Ring__and__Field_Oordered__semidom_13, cls_Product__Type_OPair__eq__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, cls_Message_Oparts_OInj_0, cls_Finite__Set_Ofinite__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, cls_List_Olength__remdups__leq_0, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Power_Orecpower_13, clsrel_Ring__and__Field_Oordered__semidom_24, cls_Event_Oevent_Oinject__3__iff1_1, clsrel_Power_Orecpower_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, clsrel_Ring__and__Field_Oordered__semiring__strict_16, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5, cls_Public_OMPair__used_1, cls_Set_OPow__iff__iff2_0, cls_List_Oappend__in__lists__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_35, clsrel_Ring__and__Field_Oordered__semiring__strict_21, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, clsarity_IntDef__Oint_59, clsarity_nat_22, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, clsrel_OrderedGroup_Ocomm__monoid__mult_3, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Message_OHPair__eq__MPair__iff1_0, cls_Datatype__Universe_OdprodE_1, clsarity_nat_44, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_3, cls_List_OlistsE_0, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Osemiring__1_3, cls_Finite__Set_Ofinite__Un__iff1_0, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, cls_Set_OUNIV__I_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, cls_Message_OCrypt__synth_1, clsrel_Ring__and__Field_Ocomm__semiring_2, cls_Public_OsymKeys__invKey__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_4, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5, cls_List_Olength__0__conv__iff2_0, clsrel_Power_Orecpower_4, cls_Divides_Odvd__0__left__iff__iff2_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0, cls_List_Oself__append__conv__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring_5, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Opordered__semiring_7, clsarity_IntDef__Oint_64, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, cls_Message_Osynth_OMPair_0, cls_Set_OUnE_0, clsrel_Ring__and__Field_Oordered__semiring__strict_11, cls_SetInterval_OatMost__eq__iff__iff1_0, cls_List_Olistrel__Cons2_0, cls_Message_OHPair__eq__MPair__iff2_0, clsarity_nat_27, cls_Relation_ODomainI_0, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, cls_Message_Omsg_Oinject__4__iff1_0, cls_Set_OinsertE_0, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_OrderedGroup_Ocomm__monoid__add_1, cls_Set_Onot__psubset__empty__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_14, clsarity_IntDef__Oint_14, clsrel_Ring__and__Field_Opordered__comm__semiring_13, clsarity_IntDef__Oint_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, clsarity_nat_16, clsrel_Ring__and__Field_Opordered__cancel__semiring_12, cls_SetInterval_OlessThan__subset__iff__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Message_Oagent_Odistinct__2__iff1_0, cls_List_Owf__lex_0, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, cls_List_Orev__is__Nil__conv__iff2_0, clsarity_nat_38, clsrel_Ring__and__Field_Ocomm__semiring__1_11, clsrel_Ring__and__Field_Osemiring__1__cancel_13, cls_Public_OpublicKey__inject__iff1_1, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, clsrel_Wellfounded__Recursion_Owellorder_3, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Ocomm__semiring__0_3, clsrel_Ring__and__Field_Oordered__semidom_8, cls_Set_OUn__empty__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_IntDef__Oint_20, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_GCD_Ogcd__dvd1_0, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, cls_SetInterval_OatMost__subset__iff__iff2_0, cls_Message_Omsg_Oinject__3__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, cls_SetInterval_Ofinite__atLeastLessThan_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, cls_Set_OUn__empty__iff1_0, clsrel_Power_Orecpower_10, 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clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_11, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2, clsarity_nat_37, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_2, cls_Set_OsingletonI_0, clsrel_LOrder_Olorder_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_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, cls_Product__Type_OPair__eq__iff1_1, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, cls_List_Orev__eq__Cons__iff__iff1_0, cls_Event_Oevent_Oinject__2__iff1_0, cls_Nat_Oadd__gr__0__iff2_1, clsrel_Ring__and__Field_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, cls_List_Osame__append__eq__iff1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, cls_Nat_Oless__Suc0__iff2_0, cls_Message_Oparts__partsD__dest_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, cls_SetInterval_OatLeast__iff__iff2_0, clsarity_IntDef__Oint_37, cls_Message_Oagent_Odistinct__1__iff1_0, cls_GCD_Ogcd__greatest__iff__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__0_10, cls_Message_OMPair__eq__HPair__iff2_0, cls_Message_Oparts_OBody__dest_0, cls_Relation_OconverseE_0, clsarity_IntDef__Oint_42, cls_IntDiv_Ozdvd__1__left_0, cls_List_Olength__greater__0__conv__iff2_0, cls_SetInterval_OatMost__subset__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_6, clsrel_Ring__and__Field_Opordered__comm__semiring_9, clsrel_Ring__and__Field_Oordered__semidom_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5, cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0, cls_GCD_Ogcd__greatest__iff__iff2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6, clsarity_nat_0, cls_Datatype__Universe_OuprodE_2, clsarity_nat_43, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_0, clsrel_Ring__and__Field_Osemiring__1_7, cls_Datatype__Universe_OIn1__not__In0__iff1_0, clsarity_IntDef__Oint_18, clsrel_LOrder_Omeet__semilorder_0, cls_List_Olist_Oinject__iff1_1, clsrel_Power_Orecpower_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_1, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, cls_Message_Omsg_Oinject__5__iff1_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring_1, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_Ring__and__Field_Ocomm__semiring__1_10, clsrel_OrderedGroup_Opordered__ab__semigroup__add_3, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8, clsrel_Ring__and__Field_Oordered__semidom_25, clsarity_IntDef__Oint_29, cls_Public_OshrK__in__used_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1, clsrel_Ring__and__Field_Osemiring__0_1, cls_GCD_Ogcd__greatest__iff__iff1_1, clsrel_Orderings_Olinorder_2, cls_Datatype__Universe_OuprodE_0, clsarity_nat_34, cls_Public_OMPair__used_0, clsarity_nat_45, 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_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_12, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsarity_set_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, cls_Message_Oin__parts__UnE_0, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Message_OMPair__analz_1, cls_Message_OHPair__neqs__6__iff1_0, clsarity_nat_17, cls_Datatype__Universe_OdprodE_2, cls_Public_OpublicKey__inject__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_5, clsrel_Ring__and__Field_Oordered__semidom_27, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Message_OCrypt__synth_0, cls_Divides_Odvd__triv__right_0, cls_List_Odistinct__remdups_0, clsrel_Ring__and__Field_Oordered__semidom_4, cls_Nat_Onot__add__less1__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4, clsarity_nat_28, clsrel_Ring__and__Field_Osemiring__0__cancel_6, clsarity_IntDef__Oint_40, clsarity_IntDef__Oint_8, clsrel_Ring__and__Field_Opordered__cancel__semiring_14, cls_Message_Omsg_Oinject__2__iff1_0, cls_Relation_Opair__in__Id__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_4, cls_Event_Oevent_Oinject__1__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16, clsrel_Ring__and__Field_Ocomm__semiring_6, cls_Set_OIntI_0, cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0, clsarity_nat_39, cls_Finite__Set_Ofinite__Union_1, clsrel_LOrder_Ojoin__semilorder_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, clsrel_OrderedGroup_Osemigroup__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20, clsarity_nat_23, cls_Yahalom_OGets__imp__analz__Spy__dest_0, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, clsrel_Ring__and__Field_Opordered__semiring_8, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8, cls_IntDiv_Ozdvd__0__left__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, clsrel_Power_Orecpower_12, cls_Message_Omsg_Oinject__6__iff1_0, cls_Nat_Oadd__gr__0__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_1, clsarity_IntDef__Oint_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9, cls_Divides_Odvd__triv__left_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3, cls_Divides_Odvd__0__right_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11, cls_Public_Oanalz__spies__pubK_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22, clsrel_Ring__and__Field_Oordered__semidom_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5, clsrel_Ring__and__Field_Osemiring__0__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_Public_Onot__symKeys__priK__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_2, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OMPair__synth__analz__iff1_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1, cls_Wellfounded__Relations_Owf__less__than_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15, cls_List_Olist_Odistinct__2__iff1_0, clsrel_Power_Orecpower_15, cls_Transitive__Closure_Or__into__rtrancl_0, clsrel_Ring__and__Field_Osemiring__1__cancel_11, clsrel_Ring__and__Field_Ocomm__semiring__0_9, clsarity_IntDef__Oint_10, clsrel_Ring__and__Field_Osemiring__0__cancel_2, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Message_Oagent_Odistinct__4__iff1_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_Event_Oevent_Odistinct__5__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_1, clsarity_IntDef__Oint_32, cls_Message_OMPair__parts_1, cls_Message_Osynth__synthD__dest_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, clsarity_nat_12, cls_List_Oappend__self__conv__iff2_0, clsarity_IntDef__Oint_22, cls_SetInterval_OgreaterThan__iff__iff1_0, cls_List_Oappend__same__eq__iff1_0, clsrel_Wellfounded__Recursion_Owellorder_2, clsarity_IntDef__Oint_5, clsarity_nat_20, cls_Set_ODiffI_0, clsrel_OrderedGroup_Oab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__semiring_4, cls_Sum__Type_OInrI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3, clsarity_fun_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4, cls_Nat_OSuc__le__mono__iff2_0, clsrel_LOrder_Ojoin__semilorder_0, cls_Public_OSpy__spies__bad__shrK_0, clsarity_IntDef__Oint_62, cls_Set_OUn__empty__iff2_0, cls_Orderings_Oorder__less__irrefl__iff1_0, cls_Public_OpublicKey__neq__privateKey__iff1_0, clsrel_Power_Orecpower_22, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1, clsrel_Ring__and__Field_Oordered__semiring__strict_14, clsarity_nat_5, cls_Datatype__Universe_Odsum__In1I_0, cls_Message_ONonce__synth_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7, cls_List_Orev__is__rev__conv__iff1_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Opordered__semiring_0, clsrel_Ring__and__Field_Opordered__comm__semiring_6, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, clsrel_Ring__and__Field_Osemiring__1_9, cls_List_Olistrel__Nil2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9, clsrel_LOrder_Olorder_1, cls_Relation_Orel__compI_0, clsarity_nat_42, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, clsrel_Ring__and__Field_Oordered__semidom_21, cls_List_Oappend__is__Nil__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_5, cls_Yahalom_Ounique__session__keys__dest_1, cls_Set_OUnionI_0, clsrel_Ring__and__Field_Ocomm__semiring__0_5, clsrel_OrderedGroup_Opordered__ab__semigroup__add_2, cls_Public_OSpy__spies__bad__privateKey_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, clsrel_Ring__and__Field_Oordered__semiring__strict_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5, clsrel_Ring__and__Field_Oordered__semiring__strict_20, cls_Message_OHPair__neqs__5__iff1_0, clsrel_Ring__and__Field_Osemiring_3, clsrel_Ring__and__Field_Opordered__semiring_11, clsarity_nat_31, cls_Datatype__Universe_OIn0__eq__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_3, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1, cls_Nat_OSuc__less__eq__iff1_0, cls_GCD_Ogcd__dvd2_0, clsrel_Power_Orecpower_8, cls_Relation_OdiagE_1, clsrel_Ring__and__Field_Oordered__semidom_26, clsrel_Ring__and__Field_Ocomm__semiring__1_6, cls_IntDiv_Ozmod__eq__0D__dest_0, cls_Event_Oevent_Oinject__2__iff1_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_6, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23, cls_Message_OMPair__synth__analz__iff2_0, clsarity_nat_9, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_Message_Oanalz__into__parts__dest_0, cls_Relation_OImage__singleton__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_10, clsrel_Ring__and__Field_Opordered__cancel__semiring_7, cls_List_ONil2__notin__lex__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_9, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9, cls_Message_OHPair__eq__MPair__iff1_1, clsrel_Ring__and__Field_Oordered__semidom_15, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14, clsarity_nat_46, cls_List_Oself__append__conv2__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_5, clsrel_Ring__and__Field_Ocomm__semiring__0_1, clsrel_Ring__and__Field_Oordered__semidom_6, clsarity_IntDef__Oint_44, cls_Nat_Oneq0__conv__iff1_0, cls_Message_OMPair__synth_1, clsrel_Power_Orecpower_2, cls_List_Olist_Odistinct__1__iff1_0, cls_Public_Ospies__pubK_0, clsrel_Ring__and__Field_Oordered__semiring__strict_23, cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, cls_List_Olistrel__Cons1_1, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Ocomm__semiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_22, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, clsrel_Ring__and__Field_Ocomm__semiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_37, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5, clsarity_nat_35, clsrel_Power_Orecpower_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7, cls_Message_Osynth_OInj_0, cls_List_ONil__is__rev__conv__iff2_0, clsrel_Ring__and__Field_Opordered__comm__semiring_11, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3, cls_SetInterval_OatLeast__eq__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Message_OMPair__analz_0, clsarity_nat_8, cls_Sum__Type_OPlusE_1, cls_Set_OUnionE_0, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Osemiring__1_1, cls_Event_Oevent_Odistinct__6__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, clsrel_Ring__and__Field_Osemiring__0_4, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_List_Oin__listsI_0, cls_Divides_Odvd__1__left_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, cls_Public_OprivateKey__into__used_0, clsarity_nat_13, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Event_Oevent_Odistinct__4__iff1_0, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Message_Omsg_Oinject__6__iff1_1, cls_Message_Oagent_Odistinct__3__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Power_Orecpower_20, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Osemiring_0, clsrel_Ring__and__Field_Oordered__semidom_33, cls_Message_OHPair__neqs__2__iff1_0, cls_List_Oappend1__eq__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, cls_Public_OpublicKey__in__initState_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsarity_IntDef__Oint_11, clsrel_Ring__and__Field_Oordered__semiring__strict_13, clsrel_Ring__and__Field_Opordered__semiring_9, clsrel_Ring__and__Field_Ocomm__semiring_3, clsrel_Ring__and__Field_Osemiring__0__cancel_5, cls_Message_OFake__parts__insert__in__Un__dest_0, clsrel_Ring__and__Field_Osemiring__1__cancel_8, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6, cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, clsarity_IntDef__Oint_41, cls_Public_OpriK__in__initState_0, clsrel_Ring__and__Field_Oordered__semiring__strict_0, clsarity_nat_24, cls_Message_OHPair__eq__iff1_1, cls_Message_OKey__synth_0, clsarity_nat_1, clsrel_Power_Orecpower_11, clsrel_LOrder_Omeet__semilorder_1, cls_Message_Oanalz_ODecrypt__dest_0, clsarity_set_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0, cls_Nat_OSuc__not__Zero__iff1_0, cls_Nat_Ole0_0, clsarity_IntDef__Oint_63, cls_Event_OSpy_A_58_Abad_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, clsarity_nat_4, cls_List_ONil__is__rev__conv__iff1_0, cls_Event_Oevent_Oinject__1__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, clsrel_Wellfounded__Recursion_Owellorder_1, clsrel_OrderedGroup_Oab__semigroup__mult_1, cls_Nat_Oless__one__iff2_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, clsarity_nat_19, cls_Sum__Type_OInl__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring_0, clsrel_Ring__and__Field_Oordered__semiring__strict_15, cls_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Osemiring__0__cancel_10, clsrel_Ring__and__Field_Oordered__semidom_30, clsrel_OrderedGroup_Ocomm__monoid__mult_4, clsrel_Ring__and__Field_Osemiring__1_5, clsrel_Ring__and__Field_Ocomm__semiring__0_8, clsrel_LOrder_Olorder_3, cls_List_Olength__0__conv__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_5, clsrel_Ring__and__Field_Ocomm__semiring__1_5, clsrel_OrderedGroup_Omonoid__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2, clsrel_Ring__and__Field_Osemiring_4, clsarity_IntDef__Oint_12, clsrel_Ring__and__Field_Opordered__cancel__semiring_13, cls_Relation_OIdE_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28, clsarity_nat_2, cls_Message_Oparts__emptyE_0, clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsarity_IntDef__Oint_61, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Osemiring__0_3, cls_List_Owf__lenlex_0, clsrel_Ring__and__Field_Ocomm__semiring__1_13, cls_Public_OshrK__injective__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_7, clsrel_Ring__and__Field_Oordered__semidom_14, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, clsarity_nat_30, cls_Relation_Orel__compE_1, clsarity_set_4, clsarity_nat_41, 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, clsrel_Ring__and__Field_Osemiring__0__cancel_0, cls_List_Olength__remdups__eq__iff1_0, cls_Yahalom_OGets__imp__Says_0, cls_Message_OMPair__synth_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, cls_Set_OinsertCI_1, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Power_Orecpower_19, cls_List_Oappend__self__conv__iff1_0, cls_Public_OshrK__in__knows_0, clsrel_Ring__and__Field_Opordered__comm__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, cls_Yahalom_Ounique__session__keys__dest_2, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, clsarity_IntDef__Oint_9, cls_Public_OpubK__neq__shrK__iff1_0, cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0, clsrel_Ring__and__Field_Oordered__semiring__strict_18
% 148.81/42.57  % No. of inferences in proof: 1907
% 148.81/42.57  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 42014 ms resp. 41111 ms w/o parsing
% 149.61/42.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 149.61/42.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------