TSTP Solution File: SWV781-1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV781-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 : Fri May 19 12:18:29 EDT 2023

% Result   : Unsatisfiable 9.20s 3.08s
% Output   : Refutation 10.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  639
% Syntax   : Number of formulae    : 1183 ( 387 unt;  96 typ;   0 def)
%            Number of atoms       : 2207 ( 832 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 13688 ( 950   ~;1120   |;   0   &;11618   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  194 ( 194   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  96 usr;  12 con; 0-5 aty)
%            Number of variables   : 3512 (   0   ^;3512   !;   0   ?;3512   :)

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

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_OtakeWhile_type,type,
    c_List_OtakeWhile: $i > $i > $i > $i ).

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

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

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

thf(c_Nat_Osize__class_Osize_type,type,
    c_Nat_Osize__class_Osize: $i > $i > $i ).

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

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

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

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

thf(c_Map_Omap__upds_type,type,
    c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).

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

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

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

thf(c_List_Omap_type,type,
    c_List_Omap: $i > $i > $i > $i > $i ).

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

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

thf(class_Lattices_Oupper__semilattice_type,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

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

thf(c_List_Orotate_type,type,
    c_List_Orotate: $i > $i > $i > $i ).

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

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

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

thf(c_COMBI_type,type,
    c_COMBI: $i > $i > $i ).

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

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

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

thf(c_Message_Oagent_Oagent__case_type,type,
    c_Message_Oagent_Oagent__case: $i > $i > $i > $i > $i > $i ).

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

thf(t_a_type,type,
    t_a: $i ).

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

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

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

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

thf(class_Lattices_Olattice_type,type,
    class_Lattices_Olattice: $i > $o ).

thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xfilter__eq__Cons__iff__1__3_type,type,
    c_List_Osko__List__Xfilter__eq__Cons__iff__1__3: $i > $i > $i > $i ).

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

thf(c_Message_Oagent_Oagent__rec_type,type,
    c_Message_Oagent_Oagent__rec: $i > $i > $i > $i > $i > $i ).

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

thf(c_List_Osko__List__XCons__eq__filter__iff__1__3_type,type,
    c_List_Osko__List__XCons__eq__filter__iff__1__3: $i > $i > $i > $i ).

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

thf(c_List_Olist_Olist__case_type,type,
    c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).

thf(t_b_type,type,
    t_b: $i ).

thf(v_sko__Message__Xagent__Xsplit__1_type,type,
    v_sko__Message__Xagent__Xsplit__1: $i > $i > $i > $i ).

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

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

thf(v_sko__Message__Xagent__Xsplit__asm__1_type,type,
    v_sko__Message__Xagent__Xsplit__asm__1: $i > $i > $i > $i ).

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

thf(c_Message_Osko__Message__Xagent__Xcase__cong__1__1_type,type,
    c_Message_Osko__Message__Xagent__Xcase__cong__1__1: $i > $i > $i > $i > $i ).

thf(c_SetInterval_Oord__class_OgreaterThan_type,type,
    c_SetInterval_Oord__class_OgreaterThan: $i > $i > $i ).

thf(c_SetInterval_Oord__class_OatMost_type,type,
    c_SetInterval_Oord__class_OatMost: $i > $i > $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_Obutlast_type,type,
    c_List_Obutlast: $i > $i > $i ).

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

thf(c_SetInterval_Oord__class_OlessThan_type,type,
    c_SetInterval_Oord__class_OlessThan: $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_Olistrelp_type,type,
    c_List_Olistrelp: $i > $i > $i > $i > $o ).

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_Message_Osynth_type,type,
    c_Message_Osynth: $i > $i ).

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

thf(c_Message_Osko__Message__Xagent__Xnchotomy__1__1_type,type,
    c_Message_Osko__Message__Xagent__Xnchotomy__1__1: $i > $i ).

thf(v_sko__List__Xlist__Xinduct__2_type,type,
    v_sko__List__Xlist__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlist__Xinduct__1_type,type,
    v_sko__List__Xlist__Xinduct__1: $i > $i ).

thf(c_Message_Osko__Message__Xagent__Xexhaust__1__1_type,type,
    c_Message_Osko__Message__Xagent__Xexhaust__1__1: $i > $i ).

thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
    c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1_type,type,
    c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1: $i > $i > $i > $i > $i ).

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

thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).

thf(v_sko__Message__Xagent__Xinduct__1_type,type,
    v_sko__Message__Xagent__Xinduct__1: $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(v_sko__List__Xremove1__Xinduct__1_type,type,
    v_sko__List__Xremove1__Xinduct__1: $i > $i ).

thf(v_sko__List__Xremove1__Xinduct__2_type,type,
    v_sko__List__Xremove1__Xinduct__2: $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__2_type,type,
    v_sko__List__Xconcat__Xinduct__2: $i > $i ).

thf(c_List_Ofiltermap_type,type,
    c_List_Ofiltermap: $i > $i > $i > $i > $i ).

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

thf(v_sko__Public__XinitState__Xinduct__1_type,type,
    v_sko__Public__XinitState__Xinduct__1: $i > $i ).

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

thf(v_sko__List__Xmap__Xinduct__2_type,type,
    v_sko__List__Xmap__Xinduct__2: $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__2_type,type,
    v_sko__List__Xdistinct__Xinduct__2: $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__1_type,type,
    v_sko__List__Xconcat__Xinduct__1: $i > $i ).

thf(v_sko__Message__Xagent__Xinducts__1_type,type,
    v_sko__Message__Xagent__Xinducts__1: $i > $i ).

thf(v_sko__List__Xmap__Xinduct__1_type,type,
    v_sko__List__Xmap__Xinduct__1: $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__1_type,type,
    v_sko__List__Xdistinct__Xinduct__1: $i > $i ).

thf(c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1_type,type,
    c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1: $i > $i > $i > $i > $i ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(1501,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1411,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)],[371]) ).

thf(37,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ A @ C @ D ) ) )
      | ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__Cons__iff_5) ).

thf(629,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ A @ C @ D ) ) )
      | ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(391,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1454,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)],[391]) ).

thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).

thf(846,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)],[121]) ).

thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(1031,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)],[199]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
      = ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).

thf(893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
      = ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1315,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)],[330]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(962,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(161,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ F @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_7) ).

thf(941,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ F @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(1179,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)],[266]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__iff_1) ).

thf(1322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(196,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ F @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_3) ).

thf(1024,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ F @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1469,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)],[398]) ).

thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(1168,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)],[260]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_remove1__append_0) ).

thf(760,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)],[87]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(231,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(1105,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
        = A )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
        = A )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).

thf(555,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(275,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).

thf(1200,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)],[275]) ).

thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).

thf(1211,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)],[280]) ).

thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).

thf(582,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)],[19]) ).

thf(458,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_9) ).

thf(1596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(423,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1522,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

thf(1443,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)],[386]) ).

thf(467,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
        = ( c_Message_Oagent_Oagent__case @ F @ G @ H @ D @ E ) )
      | ( D = c_Message_Oagent_OSpy )
      | ( D
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ G @ E ) ) )
      | ( D = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_0) ).

thf(1618,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
        = ( c_Message_Oagent_Oagent__case @ F @ G @ H @ D @ E ) )
      | ( D = c_Message_Oagent_OSpy )
      | ( D
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ G @ E ) ) )
      | ( D = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(183,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
      | ~ ( c_List_Olistrelp @ A @ C @ F @ D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).

thf(994,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
      | ~ ( c_List_Olistrelp @ A @ C @ F @ D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(445,axiom,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1569,plain,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).

thf(1544,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)],[434]) ).

thf(522,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).

thf(1728,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).

thf(873,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)],[131]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xinduct__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinduct_0) ).

thf(1142,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xinduct__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(677,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)],[55]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_3) ).

thf(1305,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(1173,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)],[263]) ).

thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).

thf(730,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)],[77]) ).

thf(317,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).

thf(1290,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)],[317]) ).

thf(80,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).

thf(741,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(218,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( c_Message_Oagent_OFriend @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I7_J_0) ).

thf(1073,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( c_Message_Oagent_OFriend @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).

thf(1041,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)],[203]) ).

thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(861,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)],[127]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1705,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1655,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)],[487]) ).

thf(247,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/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(1137,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)],[247]) ).

thf(525,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1735,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)],[525]) ).

thf(290,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/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).

thf(1233,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)],[290]) ).

thf(335,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1327,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)],[335]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(416,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).

thf(1507,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(534,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1756,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)],[534]) ).

thf(327,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1310,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(536,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/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1761,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)],[536]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).

thf(1342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(913,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)],[149]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OServer @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I8_J_0) ).

thf(829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OServer @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(142,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).

thf(898,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1001,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)],[186]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).

thf(1127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(449,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/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).

thf(1576,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)],[449]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_0) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(401,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(1475,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)],[401]) ).

thf(483,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

thf(1650,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)],[483]) ).

thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1645,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)],[480]) ).

thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1518,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)],[421]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(469,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/sandbox2/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).

thf(1623,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)],[469]) ).

thf(405,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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1482,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)],[405]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(1254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1628,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)],[472]) ).

thf(12,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(570,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(490,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).

thf(1660,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)],[490]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).

thf(719,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)],[72]) ).

thf(336,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).

thf(1330,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(802,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)],[102]) ).

thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(1055,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)],[210]) ).

thf(370,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1409,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(329,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1313,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)],[329]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(1279,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1462,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)],[395]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).

thf(1059,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(902,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)],[144]) ).

thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(638,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)],[40]) ).

thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_3) ).

thf(1087,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)],[223]) ).

thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1247,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)],[296]) ).

thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_1) ).

thf(1115,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)],[236]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

thf(1773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).

thf(606,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)],[29]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(1347,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1572,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)],[447]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(134,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).

thf(881,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)],[134]) ).

thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1489,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)],[408]) ).

thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(1714,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)],[515]) ).

thf(98,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(789,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)],[98]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

thf(623,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)],[35]) ).

thf(159,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).

thf(937,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(905,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(1109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__iff_0) ).

thf(1682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(359,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/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1383,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)],[359]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1020,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).

thf(574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(167,axiom,
    ! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).

thf(956,plain,
    ! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(425,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).

thf(998,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)],[185]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).

thf(1405,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)],[368]) ).

thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(1600,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)],[460]) ).

thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(981,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)],[178]) ).

thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(766,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)],[90]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__fun__def_1) ).

thf(1119,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(93,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_6) ).

thf(774,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(506,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1697,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)],[506]) ).

thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1242,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)],[294]) ).

thf(122,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

thf(849,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)],[122]) ).

thf(462,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).

thf(1604,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)],[462]) ).

thf(152,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( c_Message_Oagent_OFriend @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I2_J_0) ).

thf(920,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( c_Message_Oagent_OFriend @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Notes__rev_1) ).

thf(1153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1338,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)],[339]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(328,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(1311,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)],[328]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xexhaust__1__1 @ A ) ) )
      | ( A = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oexhaust_0) ).

thf(1067,plain,
    ! [A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xexhaust__1__1 @ A ) ) )
      | ( A = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(476,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(1636,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)],[476]) ).

thf(383,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/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

thf(1438,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)],[383]) ).

thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).

thf(661,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)],[49]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).

thf(546,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(99,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(793,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)],[99]) ).

thf(539,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/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(1768,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)],[539]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_8) ).

thf(714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(206,axiom,
    ! [A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xnchotomy__1__1 @ A ) ) )
      | ( A = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Onchotomy_0) ).

thf(1047,plain,
    ! [A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xnchotomy__1__1 @ A ) ) )
      | ( A = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).

thf(1730,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)],[523]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1057,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(258,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/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(1163,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)],[258]) ).

thf(310,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_0) ).

thf(1274,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)],[310]) ).

thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(746,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)],[82]) ).

thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(825,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)],[113]) ).

thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).

thf(952,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)],[165]) ).

thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

thf(1580,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)],[451]) ).

thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(1123,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)],[240]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I10_J_0) ).

thf(1570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(407,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/sandbox2/benchmark/theBenchmark.p',cls_set__update__subsetI_0) ).

thf(1487,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)],[407]) ).

thf(62,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).

thf(693,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)],[62]) ).

thf(354,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).

thf(1370,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)],[354]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Gets__rev_0) ).

thf(1238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(361,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1387,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)],[361]) ).

thf(520,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1723,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)],[520]) ).

thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(910,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)],[148]) ).

thf(168,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/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(957,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)],[168]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_5) ).

thf(1751,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).

thf(820,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)],[110]) ).

thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1423,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)],[375]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).

thf(566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(1365,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)],[352]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1296,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

thf(1687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(470,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).

thf(1624,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1159,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)],[256]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).

thf(1656,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(86,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( c_in @ F @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).

thf(757,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( c_in @ F @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I13_J_0) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(68,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(710,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).

thf(974,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)],[175]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(1012,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)],[190]) ).

thf(220,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).

thf(1079,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)],[220]) ).

thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

thf(1027,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)],[197]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).

thf(682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Orev @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

thf(1195,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)],[273]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__subset__iff_0) ).

thf(1407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__append_0) ).

thf(1634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(363,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/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1392,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)],[363]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(350,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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1360,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)],[350]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OServer @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I1_J_0) ).

thf(948,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OServer @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).

thf(725,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)],[75]) ).

thf(412,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ H @ B @ D ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_2) ).

thf(1498,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ H @ B @ D ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I3_J_0) ).

thf(593,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(869,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)],[130]) ).

thf(181,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
      | ( A = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ F @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_1) ).

thf(989,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
      | ( A = c_Message_Oagent_OServer )
      | ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
        = ( c_Message_Oagent_Oagent__case @ G @ C @ F @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1592,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)],[456]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).

thf(578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(1089,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)],[224]) ).

thf(432,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(1541,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).

thf(1259,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)],[302]) ).

thf(429,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/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1534,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)],[429]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OServer @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_0) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OServer @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(356,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1375,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)],[356]) ).

thf(239,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/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).

thf(1121,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)],[239]) ).

thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(1111,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)],[234]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(1227,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).

thf(1096,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)],[227]) ).

thf(495,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(1672,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)],[495]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(237,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(1118,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(884,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)],[135]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I6_J_0) ).

thf(1082,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).

thf(686,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)],[59]) ).

thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1424,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)],[376]) ).

thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).

thf(642,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)],[42]) ).

thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

thf(1414,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)],[372]) ).

thf(508,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xinducts__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinducts_0) ).

thf(1700,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xinducts__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).

thf(1214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(529,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
        = ( c_Message_Oagent_Oagent__case @ A @ F @ G @ D @ E ) )
      | ( D = c_Message_Oagent_OSpy )
      | ( D
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ F @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_4) ).

thf(1744,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
        = ( c_Message_Oagent_Oagent__case @ A @ F @ G @ D @ E ) )
      | ( D = c_Message_Oagent_OSpy )
      | ( D
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ F @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(278,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).

thf(1207,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(23,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/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).

thf(590,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)],[23]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I10_J_0) ).

thf(1612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(202,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(1039,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).

thf(970,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)],[173]) ).

thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).

thf(837,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)],[118]) ).

thf(334,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/sandbox2/benchmark/theBenchmark.p',cls_filter__empty__conv_0) ).

thf(1324,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)],[334]) ).

thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).

thf(1297,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)],[321]) ).

thf(289,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/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(1231,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)],[289]) ).

thf(493,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1668,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)],[493]) ).

thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1192,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)],[271]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(984,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)],[179]) ).

thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__filter_0) ).

thf(721,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)],[73]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(459,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1599,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(518,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1720,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

thf(1759,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)],[535]) ).

thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).

thf(647,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)],[44]) ).

thf(543,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1776,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)],[543]) ).

thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(1263,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)],[304]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(228,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(253,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_5) ).

thf(1150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

thf(1478,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)],[403]) ).

thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1530,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)],[427]) ).

thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(1456,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)],[392]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(1333,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Public__XinitState__Xinduct__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState_Oinduct_0) ).

thf(1434,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OSpy ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_OFriend @ ( v_sko__Public__XinitState__Xinduct__1 @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Message_Oagent_OServer ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).

thf(1318,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)],[331]) ).

thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(1202,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)],[276]) ).

thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(805,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)],[104]) ).

thf(505,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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1695,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)],[505]) ).

thf(443,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oremdups @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).

thf(1563,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)],[443]) ).

thf(261,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(1170,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(1286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_1) ).

thf(1466,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)],[397]) ).

thf(491,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1663,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(419,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1515,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)],[419]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(888,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)],[137]) ).

thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).

thf(1732,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)],[524]) ).

thf(154,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(926,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(514,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1712,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)],[514]) ).

thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).

thf(1054,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)],[209]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(1187,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)],[269]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(674,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(33,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).

thf(618,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)],[33]) ).

thf(498,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(1680,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)],[498]) ).

thf(283,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(1219,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)],[283]) ).

thf(309,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Orev @ A @ tc_Event_Oevent ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__spies__evs__revD2_0) ).

thf(1273,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Orev @ A @ tc_Event_Oevent ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(530,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1747,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)],[530]) ).

thf(436,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_2) ).

thf(1548,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)],[436]) ).

thf(125,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_10) ).

thf(856,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(14,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(573,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(60,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).

thf(689,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

thf(733,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)],[78]) ).

thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).

thf(601,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)],[27]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).

thf(1135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(482,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(1648,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(83,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_10) ).

thf(750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).

thf(1510,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)],[417]) ).

thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(1146,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)],[251]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).

thf(1754,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(507,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(1698,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(1103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).

thf(584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1007,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)],[188]) ).

thf(120,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_8) ).

thf(843,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(92,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(772,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(484,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1652,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)],[484]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).

thf(1520,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)],[422]) ).

thf(466,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_7) ).

thf(1615,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(362,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/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1389,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)],[362]) ).

thf(378,axiom,
    c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).

thf(1428,plain,
    c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(494,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Nil__conv_0) ).

thf(1669,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)],[494]) ).

thf(232,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/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(1107,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)],[232]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Orev @ A @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__evs__rev_0) ).

thf(1092,plain,
    ! [A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Orev @ A @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(1464,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)],[396]) ).

thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1356,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)],[348]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(1675,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)],[496]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Notes__rev_0) ).

thf(1139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(414,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1503,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(764,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(272,axiom,
    ! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).

thf(1194,plain,
    ! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(143,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(900,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)],[143]) ).

thf(116,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ F @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_5) ).

thf(831,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ F @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1574,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).

thf(1349,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)],[345]) ).

thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_2) ).

thf(996,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)],[184]) ).

thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1542,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)],[433]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).

thf(1144,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)],[250]) ).

thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(649,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)],[45]) ).

thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(616,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)],[32]) ).

thf(503,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).

thf(1690,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)],[503]) ).

thf(26,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_1) ).

thf(599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(540,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funI_0) ).

thf(1771,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(737,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)],[79]) ).

thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(890,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)],[138]) ).

thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(1471,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)],[399]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

thf(1339,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)],[340]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1630,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)],[473]) ).

thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(799,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)],[101]) ).

thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(964,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)],[171]) ).

thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).

thf(1022,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)],[195]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremove1 @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remove1_1) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremove1 @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

thf(1177,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)],[265]) ).

thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).

thf(1061,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)],[213]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThan @ B @ A )
       != ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThan__eq__iff_0) ).

thf(858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThan @ B @ A )
       != ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(1557,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)],[440]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
      | ( ( c_List_Oremdups @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).

thf(552,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
      | ( ( c_List_Oremdups @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(1029,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)],[198]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(895,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)],[140]) ).

thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_remove1__append_1) ).

thf(626,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)],[36]) ).

thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).

thf(915,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)],[150]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeast @ B @ A )
       != ( c_SetInterval_Oord__class_OatLeast @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeast @ B @ A )
       != ( c_SetInterval_Oord__class_OatLeast @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(1460,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)],[394]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1198,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(457,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(1594,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(1015,plain,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).

thf(986,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)],[180]) ).

thf(542,axiom,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1775,plain,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(298,axiom,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1250,plain,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1496,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(46,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_in @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ A @ C @ D ) @ ( c_List_Oset @ C @ D ) @ D )
      | ( ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D )
        = ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filter__iff_4) ).

thf(653,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_in @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ A @ C @ D ) @ ( c_List_Oset @ C @ D ) @ D )
      | ( ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D )
        = ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).

thf(658,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( c_List_Odistinct @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I3_J_0) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(39,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/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).

thf(636,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)],[39]) ).

thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(1044,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)],[204]) ).

thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).

thf(1445,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)],[387]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

thf(1528,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(95,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).

thf(780,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)],[95]) ).

thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1643,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)],[479]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).

thf(563,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(1076,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)],[219]) ).

thf(471,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1626,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)],[471]) ).

thf(452,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).

thf(1583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

thf(1166,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)],[259]) ).

thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(944,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)],[162]) ).

thf(56,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I9_J_0) ).

thf(680,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_2) ).

thf(1420,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)],[374]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).

thf(927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(501,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).

thf(1684,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)],[501]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(1277,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)],[311]) ).

thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(1134,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)],[245]) ).

thf(160,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).

thf(939,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(663,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)],[50]) ).

thf(3,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(548,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(968,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)],[172]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(112,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).

thf(823,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(1547,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)],[435]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(580,plain,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_1) ).

thf(1516,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(41,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I2_J_0) ).

thf(640,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

thf(1070,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)],[217]) ).

thf(444,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/sandbox2/benchmark/theBenchmark.p',cls_last__in__set_0) ).

thf(1566,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)],[444]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1647,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)],[481]) ).

thf(306,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_7) ).

thf(1267,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1484,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).

thf(712,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)],[69]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).

thf(557,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).

thf(705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_1) ).

thf(1156,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)],[255]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).

thf(1225,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)],[286]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(166,axiom,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).

thf(954,plain,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
      = ( c_Event_OinitState @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).

thf(1716,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)],[516]) ).

thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).

thf(1452,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)],[390]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(717,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(537,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_9) ).

thf(1763,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(431,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

thf(1538,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)],[431]) ).

thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).

thf(1130,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)],[243]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(1085,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(576,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)],[16]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(1658,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(1,negated_conjecture,
    ~ ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_OtakeWhile @ v_P @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(544,plain,
    ~ ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_OtakeWhile @ v_P @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(907,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1358,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)],[349]) ).

thf(81,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).

thf(744,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

thf(1766,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).

thf(1257,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)],[301]) ).

thf(430,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/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

thf(1536,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)],[430]) ).

thf(47,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/sandbox2/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).

thf(656,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)],[47]) ).

thf(509,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/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).

thf(1702,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)],[509]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).

thf(1052,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)],[208]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).

thf(571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

thf(876,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)],[132]) ).

thf(293,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1240,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)],[293]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OSpy @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_2) ).

thf(1221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OSpy @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__subset__iff_1) ).

thf(1284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(531,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1749,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)],[531]) ).

thf(377,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(1427,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).

thf(1585,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)],[453]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(978,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(308,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1272,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(612,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)],[31]) ).

thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1459,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)],[393]) ).

thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(931,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)],[157]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(53,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ A @ C @ D ) ) )
      | ( ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D )
        = ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filter__iff_5) ).

thf(671,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ A @ C @ D ) ) )
      | ( ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D )
        = ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(976,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(486,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1654,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).

thf(1216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(1126,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)],[241]) ).

thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).

thf(1448,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)],[388]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).

thf(1590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(402,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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1476,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)],[402]) ).

thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1639,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)],[477]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

thf(1101,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(632,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)],[38]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I14_J_0) ).

thf(1523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(786,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)],[97]) ).

thf(22,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_1) ).

thf(588,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).

thf(699,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)],[64]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).

thf(813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(519,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

thf(1721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).

thf(1341,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)],[341]) ).

thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(896,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)],[141]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1491,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(319,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1294,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

thf(1308,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)],[326]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).

thf(684,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(4,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).

thf(549,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(1045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(1161,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)],[257]) ).

thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).

thf(1440,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)],[384]) ).

thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(929,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)],[156]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(1607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).

thf(763,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)],[88]) ).

thf(34,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(620,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)],[34]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(1725,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)],[521]) ).

thf(450,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/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).

thf(1578,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)],[450]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).

thf(1678,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)],[497]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).

thf(950,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)],[164]) ).

thf(288,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/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(1229,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)],[288]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Oset @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Oset @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(358,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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1380,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)],[358]) ).

thf(252,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).

thf(1148,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
      | ~ ( c_List_Odistinct @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).

thf(867,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)],[129]) ).

thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__append1_0) ).

thf(603,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)],[28]) ).

thf(478,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(1642,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)],[478]) ).

thf(84,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_6) ).

thf(752,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

thf(854,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)],[124]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(865,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)],[128]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

thf(1436,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)],[382]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remdups_0) ).

thf(918,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)],[151]) ).

thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).

thf(1363,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)],[351]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(1561,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(114,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(828,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(1065,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)],[215]) ).

thf(63,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_4) ).

thf(696,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(464,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/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1610,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)],[464]) ).

thf(100,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_4) ).

thf(796,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_2) ).

thf(1335,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)],[338]) ).

thf(504,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ A ) @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).

thf(1693,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ A ) @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oagent_OFriend @ A )
       != ( c_Message_Oagent_OFriend @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinject_0) ).

thf(1033,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oagent_OFriend @ A )
       != ( c_Message_Oagent_OFriend @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(316,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).

thf(1288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(513,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ A ) @ ( v_sko__List__Xmap__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).

thf(1710,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ A ) @ ( v_sko__List__Xmap__Xinduct__2 @ A ) @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).

thf(960,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)],[169]) ).

thf(400,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/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1473,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)],[400]) ).

thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).

thf(886,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)],[136]) ).

thf(528,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/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1742,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)],[528]) ).

thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(839,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)],[119]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(1236,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1352,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)],[346]) ).

thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1261,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)],[303]) ).

thf(428,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/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1532,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)],[428]) ).

thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).

thf(596,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)],[25]) ).

thf(193,axiom,
    class_HOL_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1019,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(723,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)],[74]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(822,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)],[111]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(691,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)],[61]) ).

thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(644,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)],[43]) ).

thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(1550,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)],[437]) ).

thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).

thf(908,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)],[147]) ).

thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(992,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)],[182]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(1431,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)],[380]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(415,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(1505,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1621,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)],[468]) ).

thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(803,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)],[103]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Says__rev_0) ).

thf(1320,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate1_0) ).

thf(755,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)],[85]) ).

thf(277,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_3) ).

thf(1204,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
      | ( E = c_Message_Oagent_OSpy )
      | ( E
        = ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
      | ( E = c_Message_Oagent_OServer ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(485,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1653,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(1367,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)],[353]) ).

thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).

thf(935,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)],[158]) ).

thf(189,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_in @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ A @ C @ D ) @ ( c_List_Oset @ C @ D ) @ D )
      | ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__Cons__iff_4) ).

thf(1009,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_in @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ A @ C @ D ) @ ( c_List_Oset @ C @ D ) @ D )
      | ( ( c_List_Ofilter @ A @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ E @ D ) @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ E @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

thf(1737,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)],[526]) ).

thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1681,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)],[499]) ).

thf(268,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ G @ B @ D ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_6) ).

thf(1184,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
        = ( c_Message_Oagent_Oagent__case @ E @ C @ G @ B @ D ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(1037,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)],[201]) ).

thf(8,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

thf(560,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(1417,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)],[373]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(972,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)],[174]) ).

thf(1779,plain,
    $false,
    inference(e,[status(thm)],[1501,1718,1411,629,1190,1454,846,1031,893,1315,962,941,1179,666,1322,1665,1024,1469,1168,760,1559,1105,777,555,1200,1211,582,1596,1522,1443,1618,994,1569,1544,1728,873,1142,878,677,1305,1173,730,1290,741,1073,1041,861,1705,1655,1137,1735,1233,1327,1063,1354,1507,1756,1310,1761,1342,913,829,898,1001,1127,1576,1441,1475,1650,1645,1518,1265,1623,1482,1254,1628,570,1660,719,1330,702,802,1055,1409,1313,1279,1462,1059,1132,902,638,1087,1247,1115,1773,1494,606,1347,1572,1398,881,1489,1714,789,1450,1373,623,937,905,1109,1632,1682,834,1383,1020,574,1377,956,1526,998,1345,1405,1600,981,766,1119,774,1697,1242,849,1604,920,1153,810,1338,1708,1311,1067,1636,1438,661,546,793,1768,714,1047,1730,1057,1163,1274,746,825,952,1580,1123,1570,1487,693,1370,815,1238,1387,1723,910,957,1223,1751,820,1423,566,1602,1365,1555,1296,1687,1624,1159,1656,757,1281,710,1740,974,1012,1079,1027,682,1195,1407,1634,1392,1402,1360,948,725,1498,593,869,989,1592,578,1089,1541,1270,1259,1534,1017,1375,1121,1111,1227,1096,1672,783,1118,884,1082,1292,686,1424,642,1414,1700,1214,1744,1207,590,1612,1039,970,837,1324,1297,1231,1668,1192,1050,984,721,1429,1599,1720,1759,647,1776,1263,1588,1099,1150,1478,1530,1456,1333,1434,1318,1202,805,1695,1563,1170,1286,1466,1663,1515,586,888,1732,926,1712,1054,1187,674,618,1680,1219,1273,1747,1548,856,1301,573,689,733,601,1135,1648,750,1510,1146,1754,1698,1103,584,1007,843,772,1652,1520,1615,1389,1428,1669,1107,1092,1464,1356,1675,1139,1503,764,1194,1209,900,831,1574,1349,996,1542,1144,649,616,1690,599,1175,1771,737,890,1471,1339,609,1630,799,964,1022,668,1177,1061,858,1557,552,1029,895,626,915,769,1460,1171,1198,1594,1015,986,1775,1250,1496,851,653,658,1245,636,1044,1445,1528,780,1643,1113,563,1076,1626,1583,1166,944,680,1420,927,1684,1277,1134,939,663,548,968,1181,823,1547,580,1516,640,1070,1566,1647,1267,1484,712,557,705,1156,1225,1400,707,954,1252,1716,1452,717,1763,1538,1130,1085,576,1658,544,907,1358,744,1766,1257,1536,656,1702,1052,571,876,1240,1221,1284,1749,1427,1585,1094,978,1272,612,1459,931,1553,671,976,1654,1216,1126,1448,1590,1476,1639,1101,632,1523,786,588,699,813,1385,1721,1341,896,1491,568,1294,1308,1706,1513,684,549,1045,1161,1440,929,1607,763,620,1725,1578,1678,950,1229,1395,818,1380,1148,1248,867,603,1642,752,854,1303,865,1480,1436,918,1363,807,1561,828,1065,696,1610,796,1335,1693,1033,1288,1710,960,1473,886,1742,839,728,1236,1352,1261,1532,596,1019,723,822,1299,691,644,1550,908,992,1431,1004,1505,1621,803,1320,755,1204,1653,1367,935,1009,923,1737,1681,1184,1037,560,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV781-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n003.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 02:17:01 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.90/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.69/1.04  % [INFO] 	 Parsing done (215ms). 
% 1.69/1.05  % [INFO] 	 Running in sequential loop mode. 
% 2.17/1.25  % [INFO] 	 eprover registered as external prover. 
% 2.17/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 2.17/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.35/1.37  % [INFO] 	 Found a conjecture and 544 axioms. Running axiom selection ... 
% 2.91/1.48  % [INFO] 	 Axiom selection finished. Selected 542 axioms (removed 2 axioms). 
% 3.44/1.63  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.44/1.64  % [INFO] 	 Type checking passed. 
% 3.44/1.65  % [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 ... 
% 9.20/3.08  % External prover 'e' found a proof!
% 9.20/3.08  % [INFO] 	 Killing All external provers ... 
% 9.20/3.08  % Time passed: 2570ms (effective reasoning time: 2021ms)
% 9.20/3.08  % Solved by 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)>
% 9.20/3.08  % Axioms used in derivation (542): cls_set__subset__Cons_0, clsarity_nat__HOL_Oord, cls_butlast__snoc_0, cls_last_Osimps_0, cls_atLeastatMost__subset__iff_2, cls_agent_Ocase__cong_3, cls_sorted__append_2, cls_takeWhile__cong_1, cls_subset__insert_1, cls_ivl__disj__un_I8_J_0, cls_concat_Oinduct_1, cls_rev__swap_1, cls_last_Osimps_1, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_not__parts__not__analz_0, cls_remove1__append_0, cls_Cons__eq__append__conv_2, cls_parts_OInj_0, cls_dropWhile_Osimps_I1_J_0, cls_Un__subset__iff_0, cls_order__eq__iff_0, cls_parts__partsD_0, cls_agent_Osplit_10, cls_Cons__eq__append__conv_5, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_listrelp_OCons_0, cls_list__update__overwrite_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_knows__Notes_0, cls_butlast_Osimps_I1_J_0, cls_initState__subset__knows_0, cls_in__set__butlast__appendI_1, cls_agent_Osplit__asm_10, cls_insert__code_1, cls_dropWhile__eq__Cons__conv_0, cls_le__funD_0, cls_map__replicate_0, cls_set__ConsD_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_agent_Osplit__asm_3, cls_agent_Oinject_0, cls_atLeastLessThan__subset__iff_1, cls_list_Oinject_0, cls_filter__is__subset_0, cls_analz__subset__iff_1, cls_knows__Says_0, cls_agent_Osplit_3, cls_le__fun__def_1, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_in__set__conv__decomp_1, cls_length__remove1_1, cls_Un__commute_0, cls_Cons__eq__map__conv_3, clsarity_fun__Orderings_Oorder, cls_map_Oinduct_1, cls_map__upds__apply__nontin_0, cls_analz__cong_0, cls_rotate__map_0, cls_rev__singleton__conv_1, cls_agent_Osimps_I6_J_0, cls_agent_Ocase__cong_0, cls_UnCI_1, cls_distinct__filter_0, cls_insert__absorb_0, cls_analz__subset__parts_0, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_Fake__parts__insert_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_filter__eq__ConsD_2, cls_self__append__conv_0, cls_knows__subset__knows__Says_0, cls_sorted__Cons_2, cls_le__sup__iff_0, cls_list_Osimps_I5_J_0, 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_COMBI__def__raw_0, cls_analz__idem_0, cls_insert__subset_0, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_same__append__eq_0, clsarity_fun__Lattices_Oupper__semilattice, 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_agent_Ocase__cong_7, cls_subset__insert__iff_2, cls_Nil__is__map__conv_0, cls_synth__insert_0, cls_Un__left__commute_0, cls_agent_Osimps_I5_J_0, cls_knows__Nil_0, cls_butlast_Osimps_I2_J_1, cls_set__remove1__subset_0, cls_analz__image__freshK__simps_I61_J_0, cls_ns__sharedp_OFake_0, cls_length__map_0, cls_filter_Osimps_I2_J_0, cls_set__mp_0, cls_ivl__disj__un_I13_J_0, clsarity_bool__HOL_Oord, cls_atMost__subset__iff_1, cls_takeWhile__cong_0, cls_replicate__eq__replicate_0, cls_Server__not__bad_0, cls_agent_Osplit_8, cls_analz__image__freshK__simps_I65_J_0, cls_knows__Spy__Notes_1, cls_sorted__takeWhile_0, cls_le__supI_0, cls_sorted__Cons_3, cls_Un__subset__iff_1, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_atLeast__iff_0, cls_append__eq__append__conv2_4, cls_in__set__conv__decomp__first_2, cls_append__eq__Cons__conv_0, cls_sorted_Osimps_I3_J_1, cls_le__iff__sup_1, cls_synth__synthD_0, cls_order__eq__refl_0, cls_notin__set__remove1_0, cls_filter__append_0, cls_parts__subset__iff_1, cls_filter__eq__Cons__iff_4, cls_agent_Osimps_I9_J_0, cls_distinct_Osimps_I2_J_1, cls_le__supE_1, cls_analz__cut_0, cls_in__parts__UnE_0, cls_le__iff__sup_0, cls_distinct_Osimps_I1_J_0, cls_atLeast__subset__iff_1, cls_length__remdups__eq_0, cls_parts__mono_0, cls_in__set__conv__decomp__last_2, cls_replicate__append__same_0, cls_lessThan__subset__iff_1, cls_agent_Ocase__cong_4, cls_rev_Osimps_I2_J_0, cls_rev__map_0, cls_used__nil__subset_0, cls_atLeastatMost__subset__iff_3, clsarity_bool__Orderings_Oorder, cls_rev__singleton__conv_0, cls_takeWhile_Osimps_I1_J_0, cls_spies__Gets__rev_0, cls_concat_Oinduct_0, cls_insert__ident_0, cls_greaterThan__subset__iff_1, cls_Un__absorb2_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, cls_filter_Osimps_I1_J_0, cls_inf__sup__aci_I8_J_0, cls_agent_Osplit_2, cls_takeWhile__eq__all__conv_2, cls_listrelp_ONil_0, cls_remove1__append_1, cls_Un__upper2_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_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_distinct__map_0, cls_subset__iff_0, cls_agent_Osplit_1, 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_remove1_Oinduct_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_lessThan__eq__iff_0, cls_agent_Osplit__asm_7, cls_in__set__butlast__appendI_0, cls_filter__empty__conv_0, cls_insert__code_2, cls_in__set__replicateD_0, cls_distinct__append_0, cls_parts__Un_0, cls_map__eq__Cons__conv_3, cls_agent_Oexhaust_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_agent_Onchotomy_0, cls_spies__Notes__rev_1, cls_map__update_0, cls_append__is__Nil__conv_2, cls_list_Osplit_0, cls_append__eq__append__conv2_5, cls_synth__trans_0, cls_append__eq__Cons__conv_5, cls_Un__insert__left_0, cls_length__list__update_0, cls_analz__conj__parts_0, cls_last__in__set_0, cls_append__Nil_0, cls_map__is__Nil__conv_0, clsarity_bool__Lattices_Oupper__semilattice, 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_Fake__analz__insert_0, cls_sup__commute_0, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_set__eq__subset_2, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_length__remdups__eq_1, cls_agent_Orecs_I3_J_0, cls_greaterThan__subset__iff_0, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_filter__replicate_1, cls_dropWhile__eq__Cons__conv_2, cls_insert__subset_1, cls_map__upds__Nil2_0, cls_set__rev_0, cls_linorder__linear_0, cls_replicate__app__Cons__same_0, cls_parts__insertI_0, cls_agent_Oinduct_0, cls_rotate__simps_0, cls_atMost__subset__iff_0, cls_synth__increasing_0, cls_ns__sharedp_ONil_0, cls_Un__subset__iff_2, cls_append__eq__Cons__conv_1, cls_agent_Osplit_9, cls_Cons__eq__filter__iff_4, cls_analz_OInj_0, cls_distinct__rotate_1, clsarity_fun__Lattices_Olattice, cls_filter__replicate_0, cls_analz__parts_0, cls_fun__upds__append2__drop_0, cls_map__eq__imp__length__eq_0, cls_order__antisym_0, cls_atLeast__iff_1, cls_agent_Osimps_I3_J_0, cls_self__append__conv_1, cls_rev__filter_0, cls_set__rotate_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_atMost__eq__iff_0, cls_rotate1__is__Nil__conv_0, cls_butlast__append_0, cls_agent_Osplit__asm_6, cls_in__set__butlastD_0, cls_subset__trans_0, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_insertI1_0, cls_append__same__eq_0, clsarity_bool__Orderings_Opreorder, cls_agent_Osplit__asm_8, cls_agent_Osplit_5, cls_sup__assoc_0, cls_last__append_0, cls_list__update__swap_0, cls_length__rev_0, cls_last__snoc_0, cls_le__sup__iff_1, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_atLeast__eq__iff_0, cls_parts__cut__eq_0, cls_fun__upds__append__drop_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_sorted__Cons_0, cls_lessThan__subset__iff_0, cls_distinct1__rotate_0, cls_event_Osimps_I2_J_1, cls_append__assoc_0, cls_atLeastatMost__subset__iff_0, cls_synth__Un_0, cls_parts__cut_0, cls_atMost__iff_0, cls_sup__least_0, cls_subset__refl_0, cls_parts__subset__iff_0, cls_analz__Un_0, cls_Un__absorb1_0, cls_distinct__takeWhile_0, cls_sup1E_0, cls_agent_Ocase__cong_5, cls_butlast__append_1, cls_synth__subset__iff_1, cls_set__update__subset__insert_0, cls_agent_Osplit__asm_5, cls_map__upds__Nil1_0, cls_Spy__in__bad_0, cls_Cons__eq__append__conv_0, clsarity_nat__Lattices_Olattice, cls_sup1CI_1, cls_insertCI_0, cls_remove1_Oinduct_1, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_agent_Osplit_0, cls_takeWhile__dropWhile__id_0, cls_le__funI_0, cls_event_Osimps_I7_J_0, cls_order__eq__iff_2, cls_Fake__analz__eq_0, cls_analz__mono__contra_I2_J_0, cls_insert__mono_0, cls_le__supI2_0, cls_initState_Oinduct_0, cls_Un__assoc_0, cls_distinct__append_1, cls_event_Osimps_I1_J_1, cls_map__append_0, cls_ivl__disj__un_I10_J_0, cls_sorted__remdups_0, cls_inf__sup__ord_I4_J_0, cls_distinct__remdups__id_0, cls_agent_Osplit_6, cls_synth_OInj_0, cls_synth__idem_0, cls_sorted_Osimps_I1_J_0, cls_Un__absorb_0, cls_dropWhile__eq__Nil__conv_0, cls_order__antisym__conv_0, cls_rev__replicate_0, cls_UnE_0, cls_subset__insertI2_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_sorted__remove1_0, cls_rotate__simps_1, cls_list_Osplit__asm_1, cls_distinct__dropWhile_0, clsarity_bool__Lattices_Olattice, cls_parts__analz_0, cls_sorted__distinct__set__unique_0, cls_Cons__eq__filter__iff_5, cls_event_Osimps_I2_J_0, cls_usedI_0, cls_map__eq__conv_0, 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_sorted__append_0, cls_event_Osimps_I4_J_0, cls_rotate__is__Nil__conv_1, cls_takeWhile_Osimps_I2_J_1, cls_map__is__Nil__conv_1, cls_analz__analzD_0, cls_agent_Osplit__asm_1, cls_ivl__disj__un_I14_J_0, cls_insert__subset_2, cls_le__supI1_0, cls_sup__left__idem_0, cls_agent_Ocase__cong_2, cls_length__rotate1_0, cls_subsetD_0, cls_agent_Osimps_I8_J_0, cls_analz__synth__Un_0, cls_rev__is__Nil__conv_1, cls_parts__Un__subset2_0, cls_map_Osimps_I2_J_0, cls_le__sup__iff_2, cls_length__rotate_0, cls_set__append_0, cls_xt1_I6_J_0, cls_event_Osimps_I8_J_0, cls_dropWhile_Osimps_I2_J_1, cls_analz__mono__contra_I1_J_0, cls_insert__absorb2_0, cls_filter__eq__Cons__iff_5, cls_analz__mono_0, cls_distinct__rotate_0, cls_dropWhile__append1_0, cls_append__is__Nil__conv_1, cls_takeWhile__eq__all__conv_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_greaterThan__eq__iff_0, cls_analz__insert__eq_0, cls_atLeastatMost__subset__iff_1, cls_Un__left__absorb_0, cls_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_agent_Ocase__cong_6, cls_agent_Osimps_I7_J_0, cls_analz__analz__Un_0, cls_Nil__is__rev__conv_0, cls_synth__subset__iff_0, cls_filter__id__conv_0, clsarity_nat__Lattices_Oupper__semilattice, cls_inf__sup__ord_I3_J_0, cls_append__is__Nil__conv_0, cls_inf__sup__aci_I5_J_0, cls_knows__subset__knows__Notes_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_set__takeWhileD_1, cls_agent_Oinducts_0, cls_butlast_Osimps_I2_J_0, cls_initState__into__used_0, cls_analz__increasing_0, cls_parts__Un__subset1_0, cls_subset__insert_0, cls_sup__idem_0, cls_agent_Osplit_4, cls_Cons__eq__append__conv_4, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_distinct__remdups_0, cls_sup__ge2_0, cls_agent_Osplit__asm_9, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_rev__append_0, cls_agent_Osplit__asm_4, cls_atLeastLessThan__subset__iff_0, cls_Un__least_0, cls_Cons__eq__append__conv_1, cls_sup1CI_0, cls_map_Oinduct_0, clsarity_fun__Orderings_Opreorder, cls_remove1_Osimps_I2_J_1, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_Nil__is__append__conv_2, cls_set__takeWhileD_0, cls_insertCI_1, cls_agent_Osimps_I10_J_0, cls_knows__Spy__subset__knows__Spy__Says_0, cls_append__replicate__commute_0, cls_list_Osplit_1, cls_spies__Notes__rev_0, cls_parts__idem_0, cls_rev__swap_0, cls_analz__insertI_0, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_atMost__iff_1, cls_takeWhile_Osimps_I2_J_0, cls_subset__insertI_0, cls_length__replicate_0, cls_analz__trans_0, cls_sorted__Cons_1, cls_insert__code_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_used__Gets_0, cls_list_Oinduct_0, cls_analz__subset__cong_0, cls_agent_Orecs_I2_J_0, cls_gen__analz__insert__eq_0, cls_agent_Orecs_I1_J_0, cls_in__set__remove1_1, cls_append__eq__Cons__conv_3, cls_COMBI__def_0, cls_agent_Osplit_7, cls_insert__commute_0, cls_insert__iff_2, clsarity_nat__Orderings_Oorder, cls_agent_Osimps_I2_J_0, cls_takeWhile__eq__all__conv_1, cls_parts__synth_0, cls_Fake__parts__insert__in__Un_0, cls_append1__eq__conv_0, cls_filter_Osimps_I2_J_1, cls_Un__insert__right_0, cls_equalityE_0, cls_rev__rev__ident_0, cls_sorted__dropWhile_0, cls_atLeast__subset__iff_0, cls_event_Osimps_I5_J_0, cls_sup__absorb1_0, cls_sorted_Osimps_I3_J_0, cls_knows__Spy__Notes_0, cls_remdups__eq__nil__iff_0, cls_ivl__disj__un_I17_J_0, cls_distinct1__rotate_1, cls_distinct_Oinduct_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_spies__evs__rev_0, cls_agent_Ocase__cong_1, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_parts__spies__evs__revD2_0, cls_dropWhile_Osimps_I2_J_0, cls_list__update__nonempty_0, cls_analz__insert_0, cls_takeWhile__cong_2, cls_subset__insert__iff_1, cls_synth__mono_0, cls_remdups_Osimps_I2_J_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_spies__Says__rev_0, cls_synth__cut_0
% 9.20/3.08  % No. of inferences in proof: 1087
% 9.20/3.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2570 ms resp. 2021 ms w/o parsing
% 10.15/3.26  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.15/3.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------