TSTP Solution File: SWV772-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV772-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 05:48:36 EDT 2024

% Result   : Unsatisfiable 12.10s 4.16s
% Output   : Refutation 13.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  523
% Syntax   : Number of formulae    :  972 ( 281 unt;  75 typ;   0 def)
%            Number of atoms       : 1895 ( 622 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 11018 ( 838   ~; 998   |;   0   &;9182   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  156 ( 156   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   77 (  75 usr;  11 con; 0-5 aty)
%            Number of variables   : 2820 (   0   ^2820   !;   0   ?;2820   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Event_Oknows_type,type,
    c_Event_Oknows: $i > $i > $i ).

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

thf(c_List_Oappend_type,type,
    c_List_Oappend: $i > $i > $i > $i ).

thf(c_List_Olist_ONil_type,type,
    c_List_Olist_ONil: $i > $i ).

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

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

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

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

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

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

thf(c_Set_Oinsert_type,type,
    c_Set_Oinsert: $i > $i > $i > $i ).

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

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

thf(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: $i > $i > $i > $o ).

thf(class_Orderings_Opreorder_type,type,
    class_Orderings_Opreorder: $i > $o ).

thf(tc_bool_type,type,
    tc_bool: $i ).

thf(class_HOL_Oord_type,type,
    class_HOL_Oord: $i > $o ).

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

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

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

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

thf(c_List_Olinorder__class_Osorted_type,type,
    c_List_Olinorder__class_Osorted: $i > $i > $o ).

thf(c_List_OtakeWhile_type,type,
    c_List_OtakeWhile: $i > $i > $i > $i ).

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

thf(c_List_Oremove1_type,type,
    c_List_Oremove1: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

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

thf(c_List_Olinorder__class_Oinsort__key_type,type,
    c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i > $i > $i ).

thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(c_List_Ofilter_type,type,
    c_List_Ofilter: $i > $i > $i > $i ).

thf(c_List_Oreplicate_type,type,
    c_List_Oreplicate: $i > $i > $i > $i ).

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

thf(c_List_Olist__update_type,type,
    c_List_Olist__update: $i > $i > $i > $i > $i ).

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

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

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

thf(c_List_Osko__List__XtakeWhile__eq__all__conv__1__1_type,type,
    c_List_Osko__List__XtakeWhile__eq__all__conv__1__1: $i > $i > $i > $i ).

thf(c_List_Orotate1_type,type,
    c_List_Orotate1: $i > $i > $i ).

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

thf(c_List_Osko__List__XtakeWhile__cong__1__1_type,type,
    c_List_Osko__List__XtakeWhile__cong__1__1: $i > $i > $i > $i > $i ).

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

thf(c_List_OdropWhile_type,type,
    c_List_OdropWhile: $i > $i > $i > $i ).

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

thf(c_List_Obutlast_type,type,
    c_List_Obutlast: $i > $i > $i ).

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

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

thf(c_List_Osko__List__XCons__eq__append__conv__1__1_type,type,
    c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Otl_type,type,
    c_List_Otl: $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5_type,type,
    c_List_Osko__List__Xsplit__list__first__prop__iff__1__5: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1_type,type,
    c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5_type,type,
    c_List_Osko__List__Xsplit__list__last__prop__iff__1__5: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xrev__induct__1__2_type,type,
    c_List_Osko__List__Xrev__induct__1__2: $i > $i > $i ).

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

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

thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_type,type,
    c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Ohd_type,type,
    c_List_Ohd: $i > $i > $i ).

thf(c_List_Osko__List__Xrev__induct__1__1_type,type,
    c_List_Osko__List__Xrev__induct__1__1: $i > $i > $i ).

thf(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1_type,type,
    c_Message_Osko__Message__Xanalz__insert__eq__I__1__1: $i > $i > $i ).

thf(c_List_Osplice_type,type,
    c_List_Osplice: $i > $i > $i > $i ).

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

thf(c_List_Olist__inter_type,type,
    c_List_Olist__inter: $i > $i > $i > $i ).

thf(c_List_Oconcat__map_type,type,
    c_List_Oconcat__map: $i > $i > $i > $i > $i ).

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

thf(c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1_type,type,
    c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xrev__cases__1__1_type,type,
    c_List_Osko__List__Xrev__cases__1__1: $i > $i > $i ).

thf(c_List_Osko__List__Xrev__cases__1__2_type,type,
    c_List_Osko__List__Xrev__cases__1__2: $i > $i > $i ).

thf(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2_type,type,
    c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2: $i > $i > $i > $i ).

thf(c_List_Olast_type,type,
    c_List_Olast: $i > $i > $i ).

thf(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1_type,type,
    c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__XtakeWhile__append2__1__1_type,type,
    c_List_Osko__List__XtakeWhile__append2__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1_type,type,
    c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_NS__Shared__Mirabelle_Ons__sharedp_type,type,
    c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).

thf(c_List_Olength__unique_type,type,
    c_List_Olength__unique: $i > $i > $i ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(1190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(345,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).

thf(1237,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(379,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(1315,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(85,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ E @ B @ C @ D @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_0) ).

thf(645,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ E @ B @ C @ D @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
      = ( c_List_Ohd @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).

thf(892,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
      = ( c_List_Ohd @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(1024,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olength__unique @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olength__unique @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1083,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(468,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).

thf(1200,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).

thf(1211,plain,
    ! [A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1406,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(683,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(269,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Oset @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E )
        = ( c_Set_Oinsert @ C @ ( c_List_Oset @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__insort_0) ).

thf(1068,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Oset @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E )
        = ( c_Set_Oinsert @ C @ ( c_List_Oset @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).

thf(677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).

thf(582,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).

thf(873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(1,negated_conjecture,
    ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ v_A @ v_B @ v_X ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
   != ( c_Set_Oinsert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(449,plain,
    ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ v_A @ v_B @ v_X ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
   != ( c_Set_Oinsert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__empty__conv_0) ).

thf(1041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_1) ).

thf(861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__append2__1__1 @ A @ B @ D ) @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append2_0) ).

thf(1078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__append2__1__1 @ A @ B @ D ) @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OtakeWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).

thf(550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OtakeWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(913,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(945,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      = ( c_List_Ofilter @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).

thf(538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      = ( c_List_Ofilter @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(195,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ D @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_2) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ D @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(709,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(358,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(1265,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(368,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(1287,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(146,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(785,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(504,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(384,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(382,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1323,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(378,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      = ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).

thf(542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      = ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

thf(817,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_1) ).

thf(853,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).

thf(1087,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

thf(1362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(282,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).

thf(1100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__in__set_0) ).

thf(1232,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(1347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
      = ( c_Event_OinitState @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Nil_0) ).

thf(1415,plain,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
      = ( c_Event_OinitState @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(23,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(492,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Ohd @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).

thf(1450,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Ohd @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

thf(591,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1334,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(168,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).

thf(834,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(223,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(966,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(206,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

thf(924,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).

thf(1302,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(1151,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ ( c_List_Ohd @ D @ C ) @ ( c_List_Osplice @ B @ ( c_List_Otl @ D @ C ) @ C ) @ C ) @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ ( c_List_Ohd @ D @ C ) @ ( c_List_Osplice @ B @ ( c_List_Otl @ D @ C ) @ C ) @ C ) @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(410,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).

thf(1383,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).

thf(574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(103,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(692,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(866,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

thf(774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(998,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(766,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ D @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_1) ).

thf(687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ D @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(335,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) @ ( c_List_Oset @ D @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_3) ).

thf(1215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) @ ( c_List_Oset @ D @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 @ B @ C @ A ) @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_5) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 @ B @ C @ A ) @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(40,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
        = ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

thf(529,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
        = ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ ( c_Set_Oinsert @ C @ ( c_List_Oset @ A @ D ) @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).

thf(1067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ ( c_Set_Oinsert @ C @ ( c_List_Oset @ A @ D ) @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).

thf(793,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).

thf(1311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(263,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(1057,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Oremdups @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).

thf(910,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Oremdups @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) @ ( c_List_Oset @ D @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_4) ).

thf(825,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) @ ( c_List_Oset @ D @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(396,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1355,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).

thf(1174,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(336,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(1217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_3) ).

thf(820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(160,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_6) ).

thf(815,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(219,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat__map @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( hAPP @ A @ B ) @ ( c_List_Oconcat__map @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).

thf(957,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat__map @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( hAPP @ A @ B ) @ ( c_List_Oconcat__map @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist__inter @ B @ D @ C ) )
      | ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).

thf(894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist__inter @ B @ D @ C ) )
      | ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).

thf(746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(1091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(247,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_0) ).

thf(1021,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).

thf(778,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).

thf(1423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(11,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(467,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(1178,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).

thf(665,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(493,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(249,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(1027,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(1195,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

thf(1128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(369,axiom,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1291,plain,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(1106,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(456,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).

thf(842,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1350,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(278,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(1143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(406,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(1375,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1064,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 @ B @ C @ A ) @ ( c_List_Oset @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_4) ).

thf(980,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 @ B @ C @ A ) @ ( c_List_Oset @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(1006,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

thf(593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(869,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(610,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1118,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(416,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).

thf(1397,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Oreplicate @ B @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_0) ).

thf(519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Oreplicate @ B @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(307,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).

thf(1160,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(399,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1361,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).

thf(1292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).

thf(554,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(1182,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).

thf(1039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(224,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) @ ( c_List_Oset @ B @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_3) ).

thf(970,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) @ ( c_List_Oset @ B @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(169,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ ( c_List_OdropWhile @ A @ B @ D ) @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__append1_0) ).

thf(837,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ ( c_List_OdropWhile @ A @ B @ D ) @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).

thf(647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(409,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(1382,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(1131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1192,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(260,axiom,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).

thf(1050,plain,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(230,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(984,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(1429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( A
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

thf(1246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( A
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).

thf(503,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(515,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(359,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ E @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_2) ).

thf(1266,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ E @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(342,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1231,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1202,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(156,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).

thf(805,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_2) ).

thf(674,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).

thf(1167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(207,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ D @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ E @ F @ A ) @ F ) )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_1) ).

thf(926,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ D @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ E @ F @ A ) @ F ) )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__append2__1__1 @ A @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append2_1) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XtakeWhile__append2__1__1 @ A @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).

thf(1071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(198,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(1219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(1273,plain,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(405,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1374,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(121,axiom,
    ! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).

thf(732,plain,
    ! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(140,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(772,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_OtakeWhile @ A @ B @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).

thf(1388,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_OtakeWhile @ A @ B @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(418,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).

thf(1226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).

thf(584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

thf(1154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(184,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq__I_1) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ D @ B @ C ) @ C ) @ C )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).

thf(577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ D @ B @ C ) @ C ) @ C )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(1239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat__map @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).

thf(919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat__map @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(215,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).

thf(947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(1356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(1371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Oset @ B @ A )
       != ( c_List_Oset @ C @ A ) )
      | ~ ( c_List_Odistinct @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Odistinct @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).

thf(713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Oset @ B @ A )
       != ( c_List_Oset @ C @ A ) )
      | ~ ( c_List_Odistinct @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Odistinct @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).

thf(498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(1209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(196,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Olast @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).

thf(1408,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Olast @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(243,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).

thf(1011,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(392,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(1349,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).

thf(996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = B )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 @ A @ B @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_1) ).

thf(567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = B )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 @ A @ B @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(737,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(434,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(376,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1307,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__append_1) ).

thf(863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(764,plain,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rotate1_0) ).

thf(604,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(31,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Odistinct @ B @ C )
      | ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ D @ E @ B @ C @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_1) ).

thf(509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Odistinct @ B @ C )
      | ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ D @ E @ B @ C @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(186,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).

thf(880,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(649,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(890,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(16,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(477,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(388,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1339,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).

thf(552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(799,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(106,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ C @ E @ D )
      | ~ ( c_lessequals @ ( c_List_Oset @ A @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__update__subsetI_0) ).

thf(700,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ C @ E @ D )
      | ~ ( c_lessequals @ ( c_List_Oset @ A @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).

thf(964,plain,
    ! [A: $i] :
      ( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).

thf(943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(315,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1177,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xrev__cases__1__1 @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__cases__1__2 @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__cases_0) ).

thf(932,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xrev__cases__1__1 @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__cases__1__2 @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1061,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

thf(1198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_5) ).

thf(959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_ONil @ D ) @ D @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I1_J_0) ).

thf(1445,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_ONil @ D ) @ D @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(144,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E )
      | ~ ( c_List_Odistinct @ D @ E )
      | ( c_in @ C @ ( c_List_Oset @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_2) ).

thf(780,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Odistinct @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E )
      | ~ ( c_List_Odistinct @ D @ E )
      | ( c_in @ C @ ( c_List_Oset @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(851,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).

thf(653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(658,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(1171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(334,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_5) ).

thf(1213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) @ E )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_0) ).

thf(827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1044,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(401,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Nil__conv_0) ).

thf(1364,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1250,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).

thf(1304,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oremdups @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oremdups @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(297,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
        = A )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).

thf(617,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
        = A )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(447,axiom,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1472,plain,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(5,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(458,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(1413,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(1203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).

thf(589,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(795,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(1081,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

thf(1145,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
      | ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
      | ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
        = A )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).

thf(1400,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
        = A )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_OdropWhile @ A @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).

thf(954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_OdropWhile @ A @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).

thf(1432,plain,
    ! [A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1300,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__remdups_0) ).

thf(717,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(840,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(8,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(463,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(380,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A )
        = ( c_List_Olist_OCons @ C @ D @ E ) )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 @ C @ B @ D @ E @ A ) @ ( c_List_Oset @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__is__Cons_0) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A )
        = ( c_List_Olist_OCons @ C @ D @ E ) )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 @ C @ B @ D @ E @ A ) @ ( c_List_Oset @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(295,axiom,
    c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).

thf(1130,plain,
    c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).

thf(544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1188,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ C @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).

thf(1186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ C @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1235,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(276,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1085,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(470,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(398,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ ( c_List_OtakeWhile @ B @ A @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C ) )
      | ( ( c_List_OdropWhile @ B @ A @ C )
        = ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).

thf(1358,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ ( c_List_OtakeWhile @ B @ A @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C ) )
      | ( ( c_List_OdropWhile @ B @ A @ C )
        = ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev_0) ).

thf(744,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
      = ( c_List_Olist__update @ A @ B @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

thf(656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
      = ( c_List_Olist__update @ A @ B @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(600,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).

thf(1052,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 @ B @ C @ A ) @ ( c_List_Oset @ B @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_3) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 @ B @ C @ A ) @ ( c_List_Oset @ B @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(280,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A )
        = ( c_List_Olist_OCons @ C @ D @ E ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ ( c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 @ C @ B @ D @ E @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__is__Cons_1) ).

thf(1094,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A )
        = ( c_List_Olist_OCons @ C @ D @ E ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ ( c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 @ C @ B @ D @ E @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ ( c_List_Oremove1 @ A @ B @ D ) @ C @ D ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__append_0) ).

thf(1008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_Oappend @ ( c_List_Oremove1 @ A @ B @ D ) @ C @ D ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(177,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_6) ).

thf(859,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ A @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).

thf(991,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ B @ D @ C ) @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).

thf(1221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ B @ D @ C ) @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__in__set_0) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(442,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(1459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1180,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).

thf(524,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

thf(1453,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(426,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(465,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(976,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(903,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

thf(1062,plain,
    ! [A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(1244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).

thf(995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(221,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).

thf(961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).

thf(813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(1341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(130,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(748,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(435,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(1442,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(258,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(1045,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(667,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

thf(1294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(113,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(716,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

thf(1161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(800,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_0) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_OtakeWhile @ D @ B @ C ) )
      | ( c_in @ ( c_List_Osko__List__XtakeWhile__cong__1__1 @ A @ D @ B @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(1229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 @ B @ C @ A ) @ ( c_List_Oset @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_2) ).

thf(1395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ( c_in @ ( c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 @ B @ C @ A ) @ ( c_List_Oset @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).

thf(1380,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq__I_0) ).

thf(1148,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(950,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
      | ( ( c_List_OdropWhile @ A @ B @ C )
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).

thf(1097,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
      | ( ( c_List_OdropWhile @ A @ B @ C )
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(897,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(448,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1473,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).

thf(532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

thf(1165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).

thf(886,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(1033,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(325,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(1197,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(1268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).

thf(723,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).

thf(822,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(982,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(1120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(9,axiom,
    class_HOL_Oord @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(464,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(486,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).

thf(1320,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(187,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(882,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Orev @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

thf(940,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Orev @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(244,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(1014,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(424,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) @ ( c_List_Oset @ B @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_4) ).

thf(1417,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E ) ) )
      | ( c_in @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ A @ B @ E ) @ ( c_List_Oset @ B @ E ) @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(972,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(1476,plain,
    $false,
    inference(e,[status(thm)],[1411,629,1190,1237,1315,1110,645,892,1024,1469,1083,468,1200,1211,1005,1406,683,730,1068,677,597,1437,1158,582,873,1205,449,878,511,1041,861,1078,550,500,797,1275,472,1327,1260,913,945,670,538,1354,829,898,1001,1127,1391,782,709,1386,1265,1254,1287,570,719,785,504,1330,1323,802,1313,1455,1059,542,917,702,817,853,1087,770,1362,1100,1232,606,1347,1415,492,1450,591,623,1334,834,966,480,475,924,1302,756,1151,937,1383,574,692,866,774,1394,660,998,849,602,766,1169,687,1215,634,1074,452,529,761,1067,546,793,1311,534,1047,1057,1163,910,825,952,1355,1255,1123,1174,1217,820,788,815,957,894,746,1091,1021,778,1423,467,1032,625,1178,665,1457,522,461,493,1027,1195,1128,1291,974,1106,456,842,1350,1089,1143,1375,1064,725,980,1425,1006,1138,593,869,610,1118,989,1397,519,742,1160,488,1361,1292,554,1182,1461,642,526,1419,1016,1207,1039,970,837,647,1297,1382,1131,1192,1050,984,721,1429,1246,503,515,1249,1266,1231,1434,1202,1241,805,921,1054,1035,674,1167,586,888,926,1466,1071,906,513,1103,1219,1273,856,1374,733,562,694,732,1125,772,1388,1403,1226,584,1154,875,577,711,572,1239,1332,919,1258,947,1224,1356,540,1271,1371,713,498,1209,900,1408,1282,1011,1349,996,567,737,1439,1307,863,764,604,509,880,649,890,477,811,1339,552,799,483,700,964,915,1344,943,1177,932,1061,1198,959,1445,780,883,608,986,1113,851,653,658,685,1171,1213,827,636,1044,1364,1250,490,1304,663,1277,1134,617,1472,754,458,1413,1076,1203,589,795,680,1081,749,1145,1018,776,580,690,739,1368,993,557,1003,705,1156,1400,707,954,1252,1432,1300,791,717,840,463,1317,808,1130,1336,544,1188,1186,1262,1235,1085,470,1358,744,1141,656,613,600,1052,1427,1094,1008,859,991,1221,1284,845,1459,1180,524,495,759,1448,1453,1108,1421,465,976,903,517,1062,632,1244,786,995,961,813,1341,748,1030,929,478,832,1442,1045,667,1294,716,1161,800,1116,620,752,1280,1229,1395,1380,1148,735,950,1097,564,506,897,1473,532,696,1165,886,1033,1197,1268,1378,459,908,723,822,982,871,1120,728,740,1352,464,486,1320,935,1184,1463,639,454,882,1367,940,1037,560,1014,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWV772-1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n010.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 08:15:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.89/1.25  % [INFO] 	 Parsing done (300ms). 
% 1.89/1.26  % [INFO] 	 Running in sequential loop mode. 
% 2.65/1.62  % [INFO] 	 eprover registered as external prover. 
% 2.65/1.63  % [INFO] 	 cvc4 registered as external prover. 
% 2.65/1.63  % [INFO] 	 Scanning for conjecture ... 
% 3.07/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 449 axioms. Running axiom selection ... 
% 3.55/1.95  % [INFO] 	 Axiom selection finished. Selected 447 axioms (removed 2 axioms). 
% 4.28/2.16  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.28/2.18  % [INFO] 	 Type checking passed. 
% 4.28/2.18  % [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 ... 
% 12.10/4.15  % External prover 'e' found a proof!
% 12.10/4.15  % [INFO] 	 Killing All external provers ... 
% 12.10/4.16  % Time passed: 3685ms (effective reasoning time: 2886ms)
% 12.10/4.16  % Axioms used in derivation (447): cls_set__subset__Cons_0, clsarity_nat__HOL_Oord, cls_butlast__snoc_0, cls_Nil__is__rev__conv_1, cls_Crypt__notin__initState_0, cls_last_Osimps_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_sorted__append_2, cls_parts_OBody_0, cls_takeWhile__cong_1, cls_subset__insert_1, cls_last_Osimps_1, cls_order__le__less__trans_0, cls_rev__swap_1, cls_not__parts__not__analz_0, cls_remove1__append_0, cls_Cons__eq__append__conv_2, cls_dropWhile_Osimps_I1_J_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_parts__partsD_0, cls_Cons__eq__append__conv_5, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_less__fun__def_1, cls_list__update__overwrite_0, cls_splice_Osimps_I2_J_1, cls_xt1_I12_J_0, cls_knows__Notes_0, cls_set__ConsD_0, cls_insort__key_Osimps_I2_J_1, cls_butlast_Osimps_I1_J_0, cls_initState__subset__knows_0, cls_in__set__butlast__appendI_1, cls_split__list__last__prop__iff_4, cls_insert__code_1, cls_dropWhile__eq__Cons__conv_0, cls_splice__Cons__Cons_0, cls_le__funD_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_list_Oinject_0, cls_filter__is__subset_0, cls_analz__subset__iff_1, cls_Says__imp__used_0, cls_knows__Says_0, cls_tl_Osimps_I1_J_0, cls_linorder__neqE_0, cls_rev__induct_0, cls_in__set__conv__decomp_1, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_Says__imp__parts__knows__Spy_0, cls_distinct__filter_0, cls_insert__absorb_0, cls_analz__subset__parts_0, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_rev__is__rev__conv_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_set__update__subsetI_0, cls_distinct__rev_1, cls_split__list__first__prop__iff_5, cls_filter__eq__ConsD_2, cls_eq__Nil__appendI_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_knows__subset__knows__Says_0, cls_same__append__eq_0, cls_sorted__Cons_2, cls_set__rev__mp_0, cls_list__update__nonempty_1, cls_insert__iff_1, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_analz__idem_0, cls_insert__subset_0, cls_distinct__insort_2, cls_Gets__imp__knows__agents_0, cls_in__set__remove1_0, cls_knows__subset__knows__Cons_0, cls_append__Cons_0, cls_distinct_Osimps_I2_J_0, cls_takeWhile__append1_0, cls_subset__insert__iff_2, cls_hd__append_0, cls_ns__sharedp_OFake_0, cls_synth__insert_0, cls_filter_Osimps_I2_J_0, cls_knows__Nil_0, cls_butlast_Osimps_I2_J_1, cls_set__remove1__subset_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_takeWhile__cong_0, cls_replicate__eq__replicate_0, cls_Says__imp__spies_0, cls_sorted_Osimps_I3_J_1, cls_order__less__asym_0, cls_knows__Spy__Notes_1, cls_sorted__takeWhile_0, cls_linorder__not__less_0, cls_sorted__Cons_3, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_sorted__append_5, cls_append__eq__append__conv2_4, cls_in__set__conv__decomp__first_2, cls_append__eq__Cons__conv_0, cls_order__eq__refl_0, cls_notin__set__remove1_0, cls_filter__append_0, cls_msg_Osimps_I7_J_0, cls_order__le__less_0, cls_splice_Osimps_I2_J_0, cls_analz__cut_0, cls_linorder__antisym__conv1_0, cls_distinct_Osimps_I2_J_1, cls_linorder__antisym__conv2_0, cls_distinct_Osimps_I1_J_0, cls_psubset__eq_1, cls_synth__synthD_0, cls_order__less__asym_H_0, cls_parts__subset__iff_1, cls_takeWhile_Osimps_I1_J_0, cls_insert__ident_0, cls_split__list__last__prop__iff_5, cls_parts__mono_0, cls_in__set__conv__decomp__last_2, cls_replicate__append__same_0, cls_rev_Osimps_I2_J_0, clsarity_bool__Orderings_Oorder, cls_filter_Osimps_I1_J_0, cls_rev__induct_1, cls_sorted__append_3, cls_rev__singleton__conv_0, cls_hd__append_1, cls_used__nil__subset_0, cls_psubset__trans_0, cls_distinct__remove1_0, cls_less__le__not__le_2, cls_xt1_I10_J_0, cls_takeWhile__eq__all__conv_2, cls_parts__knows__Spy__subset__used_0, cls_remove1__append_1, cls_not__less__iff__gr__or__eq_0, cls_remdups_Osimps_I2_J_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_subset__iff_0, cls_distinct__append_0, cls_takeWhile__tail_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_Cons__eq__append__conv_3, cls_event_Osimps_I6_J_0, cls_self__append__conv2_1, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_sorted_Osimps_I3_J_2, cls_in__set__butlast__appendI_0, cls_filter__empty__conv_0, cls_self__append__conv2_0, cls_insort__key_Osimps_I2_J_0, cls_insert__code_2, cls_in__set__replicateD_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_append__is__Nil__conv_2, cls_analz__conj__parts_0, cls_split__list__first__prop__iff_6, cls_append__eq__append__conv2_5, cls_synth__trans_0, cls_append__eq__Cons__conv_5, cls_Says__imp__analz__Spy_0, cls_last__in__set_0, cls_append__Nil_0, cls_event_Osimps_I3_J_0, cls_last__append_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_set__rotate1_0, cls_xt1_I8_J_0, cls_msg_Osimps_I7_J_1, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_set__eq__subset_2, cls_knows__Gets_0, cls_insert__subset_1, cls_filter__replicate_1, cls_dropWhile__eq__Cons__conv_2, cls_set__rev_0, cls_hd__dropWhile_0, cls_linorder__linear_0, cls_parts__insertI_0, cls_rotate__simps_0, cls_synth__increasing_0, cls_filter__replicate_0, cls_append__eq__Cons__conv_1, cls_subset__iff__psubset__eq_0, cls_analz_OInj_0, cls_replicate__app__Cons__same_0, cls_distinct__insort_1, cls_ns__sharedp_ONil_0, cls_not__leE_0, cls_splice__Nil2_0, cls_analz__parts_0, cls_order__antisym_0, cls_rotate1__is__Nil__conv_0, cls_butlast__append_0, cls_not__Cons__self_0, cls_sorted__append_4, cls_self__append__conv_1, cls_rev__filter_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_in__set__butlastD_0, cls_subset__trans_0, cls_insertI1_0, cls_linorder__antisym__conv1_1, cls_psubset__insert__iff_6, cls_append__same__eq_0, cls_analz__insert__Crypt__subset_0, clsarity_bool__Orderings_Opreorder, cls_analz__insert__cong_0, cls_parts__cut__eq_0, cls_splice_Osimps_I1_J_0, cls_Nil__is__append__conv_1, cls_last__append_0, cls_list__update__swap_0, cls_last__snoc_0, cls_mem__def_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_append__assoc_0, cls_distinct__takeWhile_0, cls_concat__map_Osimps_I2_J_0, cls_set__insort_0, cls_subset__refl_0, cls_split__list__last__prop__iff_6, cls_parts__subset__iff_0, cls_set__update__subset__insert_0, cls_event_Osimps_I2_J_1, cls_linorder__not__le_1, cls_butlast__append_1, cls_synth__subset__iff_1, cls_Spy__in__bad_0, cls_not__less__iff__gr__or__eq_1, cls_Cons__eq__append__conv_0, cls_insertCI_0, cls_psubset__eq_0, cls_takeWhile__dropWhile__id_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_Notes__imp__knows__Spy_0, cls_order__le__neq__trans_0, cls_event_Osimps_I7_J_0, cls_order__eq__iff_2, cls_linorder__antisym__conv3_0, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_insert__mono_0, cls_less__le__not__le_1, cls_list__inter_Osimps_I2_J_0, cls_distinct__append_1, cls_Fake__analz__eq_0, cls_last__rev_0, cls_event_Osimps_I1_J_1, cls_linorder__neqE__ordered__idom_0, cls_sorted__remdups_0, cls_order__neq__le__trans_0, cls_psubset__insert__iff_0, cls_distinct__remdups__id_0, cls_synth_OInj_0, cls_synth__idem_0, cls_psubset__subset__trans_0, cls_dropWhile__eq__Nil__conv_0, cls_tl__append2_0, cls_rev__replicate_0, cls_split__list__first__prop__iff_3, cls_subset__insertI2_0, cls_shrK__injective_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_sorted_Osimps_I1_J_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_distinct__dropWhile_0, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_Crypt__notin__used__empty_0, cls_takeWhile_Osimps_I2_J_1, cls_analz__analzD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_rev__eq__Cons__iff_1, cls_distinct_Osimps_I2_J_2, cls_parts__trans_0, cls_set__remdups_0, cls_psubset__insert__iff_3, cls_sorted__distinct__set__unique_0, cls_sorted__append_0, cls_event_Osimps_I4_J_0, cls_linorder__less__linear_0, cls_usedI_0, cls_insort__is__Cons_0, cls_Crypt__Spy__analz__bad_0, cls_rev__is__Nil__conv_1, cls_insert__subset_2, cls_rotate1__hd__tl_0, cls_subsetD_0, cls_distinct__insort_0, cls_xt1_I11_J_0, cls_Crypt__synth_0, cls_xt1_I6_J_0, cls_dropWhile__append1_0, cls_event_Osimps_I8_J_0, cls_dropWhile_Osimps_I2_J_1, cls_analz__mono__contra_I1_J_0, cls_event_Osimps_I1_J_2, cls_insert__absorb2_0, cls_analz__mono_0, cls_append__is__Nil__conv_1, cls_takeWhile__eq__all__conv_0, cls_analz__insert__eq_0, cls_Nil__is__rev__conv_0, cls_subset__psubset__trans_0, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_synth__subset__iff_0, cls_filter__id__conv_0, cls_append__is__Nil__conv_0, cls_insort__is__Cons_1, cls_knows__subset__knows__Notes_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_set__takeWhileD_1, cls_initState__into__used_0, cls_analz__increasing_0, cls_hd__in__set_0, cls_order__less__irrefl_0, cls_subset__insert_0, cls_Cons__eq__append__conv_4, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_butlast_Osimps_I2_J_0, cls_less__fun__def_2, cls_distinct__remdups_0, cls_hd_Osimps_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_rev__append_0, cls_analz__insert__eq__I_1, cls_Cons__eq__append__conv_1, clsarity_fun__Orderings_Opreorder, cls_remove1_Osimps_I2_J_1, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_set__takeWhileD_0, cls_insertCI_1, cls_rev__cases_0, cls_knows__Spy__subset__knows__Spy__Says_0, cls_parts__idem_0, cls_hd__rev_0, cls_rev__swap_0, cls_analz__insertI_0, cls_concat__map_Osimps_I1_J_0, cls_sorted_Osimps_I2_J_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_split__list__last__prop__iff_3, cls_tl_Osimps_I2_J_0, cls_analz__insert__eq__I_0, cls_takeWhile_Osimps_I2_J_0, cls_subset__insertI_0, cls_analz__trans_0, cls_length__unique_Osimps_I2_J_0, cls_order__less__imp__le_0, cls_Says__imp__knows_0, cls_sorted__Cons_1, cls_insert__code_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_used__Gets_0, cls_psubset__insert__iff_2, cls_list__inter_Osimps_I2_J_1, cls_split__list__first__prop__iff_4, cls_in__set__remove1_1, cls_append__eq__Cons__conv_3, cls_insert__commute_0, cls_insert__iff_2, cls_insort__key_Osimps_I1_J_0, cls_gen__analz__insert__eq_0, clsarity_nat__Orderings_Oorder, cls_takeWhile__eq__all__conv_1, cls_linorder__not__less_1, cls_append1__eq__conv_0, cls_filter_Osimps_I2_J_1, cls_takeWhile__append2_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_rev__rev__ident_0, cls_sorted__dropWhile_0, cls_distinct1__rotate_1, cls_Cons__eq__filterD_2, cls_event_Osimps_I5_J_0, cls_parts__insert__Crypt_0, cls_sorted_Osimps_I3_J_0, cls_order__less__le_1, cls_less__fun__def_0, cls_knows__imp__Says__Gets__Notes__initState_0, cls_xt1_I7_J_0, cls_knows__Spy__Notes_0, cls_remdups__eq__nil__iff_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_dropWhile_Osimps_I2_J_0, cls_psubset__eq_2, cls_synth__cut_0, cls_analz__insert_0, cls_takeWhile__cong_2, cls_synth__mono_0, cls_remdups_Osimps_I2_J_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_list__update__nonempty_0, cls_Notes__imp__knows_0, cls_takeWhile__append2_1, cls_subset__insert__iff_1
% 12.10/4.16  % No. of inferences in proof: 897
% 12.10/4.16  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3685 ms resp. 2886 ms w/o parsing
% 13.23/4.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.23/4.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------