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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL805-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:53:00 AM UTC 2026

% Result   : Unsatisfiable 21.02s 6.12s
% Output   : Refutation 22.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  917
% Syntax   : Number of formulae    : 1835 ( 625 unt;   0 typ;   0 def)
%            Number of atoms       : 3803 (1328 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 23082 (1872   ~;1968   |;   0   &;19242   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  139 ( 137 usr;  16 con; 0-6 aty)
%            Number of variables   : 5000 (   0   ^;5000   !;   0   ?;5000   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_List_Olistsp_decl,type,
    c_List_Olistsp: $i > $i > $i > $o ).

thf(c_InductTermi_OIT_decl,type,
    c_InductTermi_OIT: $i ).

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

thf(c_COMBC_decl,type,
    c_COMBC: $i > $i > $i > $i > $i > $i ).

thf(c_Lambda_Olift_decl,type,
    c_Lambda_Olift: $i ).

thf(c_HOL_Ozero__class_Ozero_decl,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

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

thf(tc_Lambda_OdB_decl,type,
    tc_Lambda_OdB: $i ).

thf(c_Lambda_Osubst_decl,type,
    c_Lambda_Osubst: $i ).

thf(v_u_____decl,type,
    v_u____: $i ).

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

thf(v_i_____decl,type,
    v_i____: $i ).

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

thf(class_Int_Onumber_decl,type,
    class_Int_Onumber: $i > $o ).

thf(tc_Int_Oint_decl,type,
    tc_Int_Oint: $i ).

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

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

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

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

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

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

thf(class_OrderedGroup_Olordered__ab__group__add__meet_decl,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

thf(class_Int_Oring__char__0_decl,type,
    class_Int_Oring__char__0: $i > $o ).

thf(class_Ring__and__Field_Oidom_decl,type,
    class_Ring__and__Field_Oidom: $i > $o ).

thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

thf(class_Divides_Oring__div_decl,type,
    class_Divides_Oring__div: $i > $o ).

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

thf(class_Int_Onumber__ring_decl,type,
    class_Int_Onumber__ring: $i > $o ).

thf(class_Divides_Osemiring__div_decl,type,
    class_Divides_Osemiring__div: $i > $o ).

thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

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

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

thf(class_OrderedGroup_Ogroup__add_decl,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

thf(class_OrderedGroup_Omonoid__add_decl,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

thf(class_Lattices_Olower__semilattice_decl,type,
    class_Lattices_Olower__semilattice: $i > $o ).

thf(class_Ring__and__Field_Omult__zero_decl,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

thf(class_OrderedGroup_Oab__group__add_decl,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

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

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

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

thf(class_Power_Opower_decl,type,
    class_Power_Opower: $i > $o ).

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

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

thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

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

thf(c_Lambda_OdB_OVar_decl,type,
    c_Lambda_OdB_OVar: $i > $i ).

thf(c_HOL_Ominus__class_Ominus_decl,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

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

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

thf(c_HOL_Oplus__class_Oplus_decl,type,
    c_HOL_Oplus__class_Oplus: $i > $i ).

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

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

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

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

thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
    c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).

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

thf(c_List_Otake_decl,type,
    c_List_Otake: $i > $i > $i > $i ).

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

thf(c_List_Odrop_decl,type,
    c_List_Odrop: $i > $i > $i > $i ).

thf(c_HOL_Oone__class_Oone_decl,type,
    c_HOL_Oone__class_Oone: $i > $i ).

thf(c_Power_Opower__class_Opower_decl,type,
    c_Power_Opower__class_Opower: $i > $i > $i > $i ).

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

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

thf(c_Type_Otype_OFun_decl,type,
    c_Type_Otype_OFun: $i > $i > $i ).

thf(c_Lambda_OdB_OApp_decl,type,
    c_Lambda_OdB_OApp: $i ).

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

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

thf(c_Type_Otyping_decl,type,
    c_Type_Otyping: $i > $i > $i > $o ).

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

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

thf(c_Fun_Ocomp_decl,type,
    c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).

thf(c_Lambda_OdB_OAbs_decl,type,
    c_Lambda_OdB_OAbs: $i > $i ).

thf(c_List_Oremove1_decl,type,
    c_List_Oremove1: $i > $i > $i > $i ).

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

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

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

thf(c_Type_Oshift_decl,type,
    c_Type_Oshift: $i > $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oring__1_decl,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

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

thf(c_Lambda_Obeta_decl,type,
    c_Lambda_Obeta: $i > $i > $o ).

thf(c_Int_Onumber__class_Onumber__of_decl,type,
    c_Int_Onumber__class_Onumber__of: $i > $i > $i ).

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

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

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

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

thf(c_Divides_Odiv__class_Omod_decl,type,
    c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).

thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
    c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).

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

thf(c_List_Ofoldl_decl,type,
    c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).

thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

thf(c_List_Olistsum_decl,type,
    c_List_Olistsum: $i > $i > $i ).

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

thf(class_Nat_Osemiring__char__0_decl,type,
    class_Nat_Osemiring__char__0: $i > $o ).

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

thf(c_Lambda_Oliftn_decl,type,
    c_Lambda_Oliftn: $i > $i > $i > $i ).

thf(c_Lambda_Osubstn_decl,type,
    c_Lambda_Osubstn: $i > $i > $i > $i ).

thf(c_List_Olistrelp_decl,type,
    c_List_Olistrelp: $i > $i > $i > $i > $o ).

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

thf(c_COMBB_decl,type,
    c_COMBB: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Type_Otypings_decl,type,
    c_Type_Otypings: $i > $i > $i > $o ).

thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_decl,type,
    c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).

thf(v_sko__List__Xlist__Xinduct__2_decl,type,
    v_sko__List__Xlist__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlist__Xinduct__1_decl,type,
    v_sko__List__Xlist__Xinduct__1: $i > $i ).

thf(v_sko__List__Xlistsp__Xcases__2_decl,type,
    v_sko__List__Xlistsp__Xcases__2: $i > $i > $i ).

thf(tc_Type_Otype_decl,type,
    tc_Type_Otype: $i ).

thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_decl,type,
    c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xmap__cong__1__1_decl,type,
    c_List_Osko__List__Xmap__cong__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xmap__eq__conv__1__1_decl,type,
    c_List_Osko__List__Xmap__eq__conv__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlistsum__map__filter__1__1_decl,type,
    c_List_Osko__List__Xlistsum__map__filter__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__List__Xlistsp__Xinduct__1_decl,type,
    v_sko__List__Xlistsp__Xinduct__1: $i > $i > $i ).

thf(v_sko__List__Xlistsp__Xinduct__2_decl,type,
    v_sko__List__Xlistsp__Xinduct__2: $i > $i > $i ).

thf(v_sko__List__Xremove1__Xinduct__1_decl,type,
    v_sko__List__Xremove1__Xinduct__1: $i > $i ).

thf(v_sko__List__Xremove1__Xinduct__2_decl,type,
    v_sko__List__Xremove1__Xinduct__2: $i > $i ).

thf(c_List_Osko__List__Xmap__idI__1__1_decl,type,
    c_List_Osko__List__Xmap__idI__1__1: $i > $i > $i > $i ).

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

thf(v_sko__List__Xlistsp__Xcases__1_decl,type,
    v_sko__List__Xlistsp__Xcases__1: $i > $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__2_decl,type,
    v_sko__List__Xconcat__Xinduct__2: $i > $i ).

thf(v_sko__List__Xtake__Xinduct__2_decl,type,
    v_sko__List__Xtake__Xinduct__2: $i > $i ).

thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_decl,type,
    c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).

thf(c_List_Olist_Olist__size_decl,type,
    c_List_Olist_Olist__size: $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_decl,type,
    c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).

thf(v_ua_______decl,type,
    v_ua______: $i ).

thf(v_sko__List__Xlistsp__Xinducts__1_decl,type,
    v_sko__List__Xlistsp__Xinducts__1: $i > $i > $i ).

thf(v_sko__List__Xlistsp__Xinducts__2_decl,type,
    v_sko__List__Xlistsp__Xinducts__2: $i > $i > $i ).

thf(v_n_____decl,type,
    v_n____: $i ).

thf(c_List_Osko__List__Xin__listsp__conv__set__1__1_decl,type,
    c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).

thf(v_sko__List__Xmap__Xinduct__2_decl,type,
    v_sko__List__Xmap__Xinduct__2: $i > $i ).

thf(c_Type_Osko__Type__Xvar__app__types__1__1_decl,type,
    c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__2_decl,type,
    v_sko__List__Xdistinct__Xinduct__2: $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__1_decl,type,
    v_sko__List__Xconcat__Xinduct__1: $i > $i ).

thf(c_List_Osko__List__Xmap__ext__1__1_decl,type,
    c_List_Osko__List__Xmap__ext__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__List__Xmap__Xinduct__1_decl,type,
    v_sko__List__Xmap__Xinduct__1: $i > $i ).

thf(v_sko__List__Xtake__Xinduct__1_decl,type,
    v_sko__List__Xtake__Xinduct__1: $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__1_decl,type,
    v_sko__List__Xdistinct__Xinduct__1: $i > $i ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

thf(2452,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(507,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).

thf(2094,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).

thf(1024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(622,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
        = C )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).

thf(2341,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
        = C )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(396,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(1840,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(689,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(2499,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(682,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(2480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Suc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
        = ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Suc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
        = ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(577,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(2250,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(1036,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(834,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(2822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(749,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

thf(2630,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(341,axiom,
    tc_Int_Oint @ class_Nat_Osemiring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).

thf(1718,plain,
    tc_Int_Oint @ class_Nat_Osemiring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(799,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(2744,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(1369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(863,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( B = D )
      | ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

thf(2889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( B = D )
      | ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(514,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(2109,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(233,axiom,
    tc_Int_Oint @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).

thf(1454,plain,
    tc_Int_Oint @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(1633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(813,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).

thf(2778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(653,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__length01_0) ).

thf(2412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(877,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2921,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(67,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(1031,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(675,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(2463,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(1899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(708,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).

thf(2544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(23,axiom,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

thf(941,plain,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(1956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(446,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1950,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(646,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

thf(2395,plain,
    v_n____ = v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(1073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(1728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).

thf(1692,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

thf(1305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(1437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(632,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(2363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).

thf(1855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).

thf(1200,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(607,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(2309,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(694,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(2512,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__append_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(559,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(2210,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(885,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(2940,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(569,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).

thf(2231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(745,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).

thf(2622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(755,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(2644,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__drop_0) ).

thf(994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(700,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(2527,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(890,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__all_0) ).

thf(2953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(731,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(2590,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1401,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

thf(2947,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(441,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(1939,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

thf(2248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(767,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(2671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(473,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(2014,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(916,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(3012,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

thf(1205,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(593,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).

thf(2282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).

thf(1591,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).

thf(2114,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(840,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(2837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1142,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(483,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(2035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(668,axiom,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(2448,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(528,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

thf(2141,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(748,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

thf(2627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(462,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1988,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(1761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(27,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).

thf(945,plain,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(486,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).

thf(2042,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

thf(1458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(723,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).

thf(2575,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(552,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).

thf(2195,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(1705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(409,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(1867,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(2184,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

thf(1164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(610,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(2316,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(2434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(785,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(2712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(1222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(12,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).

thf(930,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(630,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(2360,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).

thf(1095,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(625,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(2348,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(661,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(2432,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( A
        = ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).

thf(1441,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( A
        = ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(72,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
       != ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

thf(1046,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
       != ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1650,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(862,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).

thf(2886,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).

thf(1366,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(702,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

thf(2531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(2869,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(710,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olength__unique ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I1_J_0) ).

thf(2548,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olength__unique ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

thf(1782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

thf(2491,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(904,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

thf(2985,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(567,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
      = ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

thf(2227,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
      = ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(648,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(2400,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(1529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(426,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A
        = ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(1904,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A
        = ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).

thf(1703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(1623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(1628,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(737,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

thf(2603,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(2039,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(621,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(2339,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(411,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).

thf(1871,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(783,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(2708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(427,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping ) ) )
      | ~ ( F @ ( E @ ( tc_Type_Otype @ ( C @ ( D @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) )
      | ~ ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

thf(1907,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping ) ) )
      | ~ ( F @ ( E @ ( tc_Type_Otype @ ( C @ ( D @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) )
      | ~ ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1511,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).

thf(1826,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(1455,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(685,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).

thf(2488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(676,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(2466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(31,axiom,
    tc_Int_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

thf(949,plain,
    tc_Int_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(781,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(2703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(779,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

thf(2698,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(171,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(1298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(866,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(2897,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(16,axiom,
    tc_Int_Oint @ class_Divides_Osemiring__div,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).

thf(934,plain,
    tc_Int_Oint @ class_Divides_Osemiring__div,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(434,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(1922,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).

thf(1800,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).

thf(1147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(420,axiom,
    tc_nat @ class_Power_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(1890,plain,
    tc_nat @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(281,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).

thf(1572,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).

thf(1568,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(2520,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).

thf(2158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(1641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(603,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).

thf(2301,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

thf(1963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(703,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

thf(2533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(145,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

thf(1232,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(837,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(2829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(540,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
        = ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__all_0) ).

thf(2169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
        = ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__update_0) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_List_Orev ) @ c_List_Olistsum ) )
        = ( A @ ( B @ c_List_Olistsum ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__rev_0) ).

thf(1514,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_List_Orev ) @ c_List_Olistsum ) )
        = ( A @ ( B @ c_List_Olistsum ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(2049,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(712,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(2552,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(751,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

thf(2635,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(880,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).

thf(2929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(672,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(2456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(6,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(924,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(742,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

thf(2616,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__take_0) ).

thf(1664,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(614,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(2324,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(581,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(2259,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(759,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(2650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(571,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(2236,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(1334,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_Obeta ) )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

thf(1136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_Obeta ) )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(520,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

thf(2122,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(1828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(714,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(2555,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

thf(2073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Type_Otype @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) )
      | ( D @ ( C @ c_Type_Otype_OFun ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

thf(2017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Type_Otype @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) )
      | ( D @ ( C @ c_Type_Otype_OFun ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(544,axiom,
    tc_nat @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(2178,plain,
    tc_nat @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(2222,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(889,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).

thf(2950,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

thf(1415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).

thf(2105,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).

thf(1811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).

thf(1911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(815,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(2782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(1109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(677,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(2469,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).

thf(1151,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(19,axiom,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

thf(937,plain,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__take_0) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olistsum ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).

thf(2254,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olistsum ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).

thf(1581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(966,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(398,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

thf(1843,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(592,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(2281,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_1) ).

thf(1896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(418,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(1886,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(526,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(2137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).

thf(1351,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(443,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).

thf(1943,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(557,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(2205,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(861,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(2884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

thf(1975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(806,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
      = ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(2762,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
      = ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
      | ( C
       != ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A )
      | ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
       != D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
      | ( C
       != ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A )
      | ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
       != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(2964,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(663,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(2437,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

thf(1928,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(851,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

thf(2861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(230,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(1447,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

thf(2483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(637,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).

thf(2371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(901,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(2979,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(2002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Type_Otype_OFun ) )
       != ( D @ ( C @ c_Type_Otype_OFun ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

thf(998,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Type_Otype_OFun ) )
       != ( D @ ( C @ c_Type_Otype_OFun ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(595,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(2286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(753,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(2639,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(1697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(645,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).

thf(2392,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).

thf(2154,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

thf(1863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(2,axiom,
    tc_Int_Oint @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

thf(920,plain,
    tc_Int_Oint @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,axiom,
    tc_Int_Oint @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Lattices_Olower__semilattice) ).

thf(942,plain,
    tc_Int_Oint @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(556,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

thf(2204,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(679,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

thf(2473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(7,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

thf(925,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_Obeta ) )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

thf(1153,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_Obeta ) )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(518,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(2118,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).

thf(2047,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(796,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

thf(2737,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(754,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).

thf(2641,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).

thf(1311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

thf(2296,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(606,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(2307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(1067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(688,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).

thf(2496,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(744,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(2621,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(2660,plain,
    ! [A: $i] :
      ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

thf(1768,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(2905,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(641,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( D @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

thf(2382,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( D @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(811,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(2773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).

thf(2000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).

thf(1636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(1387,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(88,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(1091,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(1021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(590,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(2277,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).

thf(1666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(896,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).

thf(2969,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(884,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(2937,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).

thf(1824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(2132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(474,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(2015,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(768,axiom,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(2673,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(782,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(2705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(583,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(2264,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(652,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(2409,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(716,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(2560,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(826,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(2805,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(34,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

thf(952,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(706,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(2541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1570,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(1174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(141,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_1) ).

thf(1217,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(530,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

thf(2147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

thf(1883,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).

thf(1560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(293,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).

thf(1602,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

thf(1920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(681,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( G @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( F @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( F @ ( G @ ( F @ ( E @ ( D @ ( C @ c_List_Olist__update ) ) ) @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
        = ( F @ ( G @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__list__update2__drop_0) ).

thf(2477,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( G @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( F @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( F @ ( G @ ( F @ ( E @ ( D @ ( C @ c_List_Olist__update ) ) ) @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
        = ( F @ ( G @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osize_I4_J_0) ).

thf(1968,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

thf(1888,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(554,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
      = ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Orotate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).

thf(2200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
      = ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Orotate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(2179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(1195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(623,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).

thf(2344,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(1740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).

thf(974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(2958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(618,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(2332,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(836,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

thf(2826,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(833,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).

thf(2820,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(856,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__ext__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__ext__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__ext_1) ).

thf(2872,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__ext__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__ext__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_0) ).

thf(1951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(497,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

thf(2068,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(1819,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(1836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

thf(1787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(546,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(2181,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

thf(1079,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expand__Suc_0) ).

thf(2327,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(515,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(2112,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(168,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
      = ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

thf(1291,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
      = ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(809,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).

thf(2769,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(1012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(760,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(2653,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(96,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).

thf(1106,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(460,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1983,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(841,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(2840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(380,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1804,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(865,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).

thf(2895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(1498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

thf(1878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1755,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(585,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(2268,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(2515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(2100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(1851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(1772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(156,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1259,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(887,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(2946,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(906,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).

thf(2990,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(639,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(2377,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(30,axiom,
    tc_Int_Oint @ class_Power_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

thf(948,plain,
    tc_Int_Oint @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(824,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(2801,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(1953,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(202,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1375,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).

thf(2973,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(724,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

thf(2577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(1064,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

thf(1970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Type_Otype_OFun ) )
       != ( D @ ( C @ c_Type_Otype_OFun ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

thf(1227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Type_Otype_OFun ) )
       != ( D @ ( C @ c_Type_Otype_OFun ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(777,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).

thf(2694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(2509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).

thf(1672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1138,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(790,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

thf(2724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(849,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__leq_0) ).

thf(2858,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

thf(3001,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(48,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(989,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(1329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(197,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).

thf(1361,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).

thf(1659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(15,axiom,
    tc_Int_Oint @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

thf(933,plain,
    tc_Int_Oint @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(854,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

thf(2868,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(286,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(1584,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(309,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1644,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(822,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

thf(2798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(1683,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(119,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).

thf(1160,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(858,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otyping ) ) )
      | ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

thf(2877,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otyping ) ) )
      | ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(1028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(478,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_List_Olistsum ) )
        = ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_0) ).

thf(2023,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_List_Olistsum ) )
        = ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(608,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(2312,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(915,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).

thf(3010,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(671,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

thf(2455,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(741,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(2613,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

thf(1791,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(541,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( D @ ( C @ ( A @ c_List_Olist_Olist__size ) ) @ ( B @ ( A @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osize_I2_J_0) ).

thf(2172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( D @ ( C @ ( A @ c_List_Olist_Olist__size ) ) @ ( B @ ( A @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(1114,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).

thf(1776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(605,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

thf(2304,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).

thf(1539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(843,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

thf(2845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(1668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(574,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(2243,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(2006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(718,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(2566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(445,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__cong__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__cong__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__cong_1) ).

thf(1947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__cong__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__cong__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(830,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(2813,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(412,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(1874,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(1715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(804,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).

thf(2756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(1525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(521,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(2125,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(704,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).

thf(2536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(772,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(2681,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(159,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).

thf(1266,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(868,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( E @ ( D @ ( C @ c_List_Ofilter ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
      | ( ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlistsum__map__filter__1__1 ) ) ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__map__filter_2) ).

thf(2900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( E @ ( D @ ( C @ c_List_Ofilter ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
      | ( ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlistsum__map__filter__1__1 ) ) ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(643,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(2387,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ c_Suc @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).

thf(2355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ c_Suc @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(1932,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(691,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(2505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(2766,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(491,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(2052,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(1759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(210,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

thf(1393,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

thf(1202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).

thf(1779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(558,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

thf(2208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(3,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(921,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(277,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(1563,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(820,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).

thf(2793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(465,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(1996,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).

thf(1857,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(1991,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(818,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).

thf(2788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(385,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

thf(1814,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(20,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

thf(938,plain,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
      | ~ ( B @ ( D @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

thf(1241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
      | ~ ( B @ ( D @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(2546,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__map_0) ).

thf(2057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

thf(1712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(1846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(2076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(801,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

thf(2748,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).

thf(1170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(1286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(635,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

thf(2368,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(649,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( A @ c_Type_Otyping ) ) )
      | ~ ( E @ ( D @ ( tc_Type_Otype @ ( F @ ( C @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).

thf(2402,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( A @ c_Type_Otyping ) ) )
      | ~ ( E @ ( D @ ( tc_Type_Otype @ ( F @ ( C @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(665,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

thf(2440,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(1026,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1167,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(756,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(2645,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(549,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

thf(2189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(908,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).

thf(2995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(953,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(764,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(2662,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(1185,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(657,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem0_0) ).

thf(2423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(701,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
      = ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).

thf(2529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
      = ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(8,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

thf(926,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(872,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

thf(2909,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(529,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(2144,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(792,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(2729,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1251,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(598,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

thf(2292,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(728,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).

thf(2585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(1548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(736,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

thf(2602,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

thf(1631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(770,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

thf(2677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

thf(2176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(589,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

thf(2275,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).

thf(2033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

thf(2149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(787,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(2717,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(1219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(720,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(2570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(354,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
      = ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

thf(1747,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
      = ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(480,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(2028,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(794,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__drop_0) ).

thf(2734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(1833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(791,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(2727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(431,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(1916,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(850,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).

thf(2859,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(819,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

thf(2791,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(902,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(2981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).

thf(1620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(356,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(1752,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(313,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_1) ).

thf(1652,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__eq__conv__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__eq__conv__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_2) ).

thf(1965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__eq__conv__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__eq__conv__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

thf(1520,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(525,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).

thf(2134,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(1615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(1784,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(699,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(2525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(762,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(2657,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(769,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(2674,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(719,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).

thf(2568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ c_Suc @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

thf(958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ c_Suc @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(1403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).

thf(1256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__add_0) ).

thf(1503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(2193,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(18,axiom,
    tc_Int_Oint @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Lattices_Olattice) ).

thf(936,plain,
    tc_Int_Oint @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(564,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(2220,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(615,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(2326,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olistsum ) )
        = ( A @ ( C @ c_List_Olistsum ) @ ( A @ ( B @ c_List_Olistsum ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__append_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olistsum ) )
        = ( A @ ( C @ c_List_Olistsum ) @ ( A @ ( B @ c_List_Olistsum ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(1865,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
      = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).

thf(1107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
      = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1332,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(89,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1092,plain,
    tc_Int_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(658,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

thf(2425,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(1638,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(883,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).

thf(2935,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).

thf(1733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(1239,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(466,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlistsum__map__filter__1__1 ) ) ) ) @ ( C @ hAPP ) @ hBOOL )
      | ( ( A @ ( A @ ( E @ ( E @ ( D @ ( C @ c_List_Ofilter ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__map__filter_1) ).

thf(1997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlistsum__map__filter__1__1 ) ) ) ) @ ( C @ hAPP ) @ hBOOL )
      | ( ( A @ ( A @ ( E @ ( E @ ( D @ ( C @ c_List_Ofilter ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(805,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(2759,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(803,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).

thf(2753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ c_Lambda_Obeta ) )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

thf(2166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ c_Lambda_Obeta ) )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olistsum ) )
        = ( A @ ( C @ c_List_Olistsum ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).

thf(1765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olistsum ) )
        = ( A @ ( C @ c_List_Olistsum ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(87,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(1090,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).

thf(1464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(29,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

thf(947,plain,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(722,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(2573,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(629,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(2358,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(612,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(2319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).

thf(1356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(624,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

thf(2346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(631,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).

thf(2361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(771,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).

thf(2679,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(1574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

thf(1542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(2116,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(886,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

thf(2943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_0) ).

thf(1043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(848,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(2856,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(1690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).

thf(1439,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).

thf(2065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(402,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

thf(1853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(532,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(2151,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(568,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).

thf(2229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(2084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(561,axiom,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

thf(2214,plain,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(746,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(2624,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(654,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

thf(2415,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(687,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).

thf(2493,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(2637,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).

thf(990,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__drop_0) ).

thf(996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(594,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(2284,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(580,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(2257,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1589,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(575,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

thf(2246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(249,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(1492,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(602,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(2299,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(553,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).

thf(2197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(175,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1307,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(835,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osize_I1_J_0) ).

thf(2824,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(1471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(798,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(2742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).

thf(1993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(814,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(2780,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(667,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(2446,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(674,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

thf(2461,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(784,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(2710,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).

thf(1112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(829,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(2812,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(750,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

thf(2632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(738,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).

thf(2605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(609,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(2314,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(747,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).

thf(2625,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(1909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).

thf(1162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(1838,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(1325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(732,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

thf(2593,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(913,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

thf(3006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).

thf(964,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ ( A @ c_List_Olength__unique ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__length__unique_0) ).

thf(1460,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ ( A @ c_List_Olength__unique ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(757,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(2647,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(25,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

thf(943,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(578,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).

thf(2252,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(842,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(2842,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(14,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(932,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(655,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(2418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(1841,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(633,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(2365,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(2212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(839,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(2835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(504,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(2086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(527,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(2139,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(126,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

thf(1176,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(604,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(2303,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(490,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).

thf(2051,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(711,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(2550,plain,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(636,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(2369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

thf(1015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(881,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).

thf(2931,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(596,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(2288,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1364,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(895,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(2967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(910,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).

thf(2999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(534,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(2156,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(4,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).

thf(922,plain,
    tc_Int_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(776,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__filter__le_0) ).

thf(2693,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(903,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(2984,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).

thf(1805,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(1076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

thf(2054,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(383,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__map_0) ).

thf(1809,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(2096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(513,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(2107,plain,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

thf(2471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(669,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(2449,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(879,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(2927,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(21,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

thf(939,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(867,axiom,
    tc_nat @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(2899,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(968,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(726,axiom,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(2582,plain,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).

thf(1049,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1626,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(914,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(3009,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).

thf(1034,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(572,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

thf(2239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(874,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(2914,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(831,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(2816,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(26,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

thf(944,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(765,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(2665,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(611,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(2318,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(816,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

thf(2784,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

thf(2271,plain,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(9,axiom,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__meet,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__meet) ).

thf(927,plain,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__meet,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(484,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

thf(2037,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(773,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(2684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(555,axiom,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

thf(2202,plain,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(734,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

thf(2597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__id_0) ).

thf(1958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

thf(1961,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ c_List_Olist_ONil ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).

thf(2397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ c_List_Olist_ONil ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1070,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(900,axiom,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(2977,plain,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(352,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1743,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(793,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(2732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(788,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

thf(2720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(1531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(860,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(2882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(377,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(1798,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(601,axiom,
    tc_nat @ class_Nat_Osemiring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(2298,plain,
    tc_nat @ class_Nat_Osemiring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).

thf(1003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(365,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).

thf(1770,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(1566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(472,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

thf(2012,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(294,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).

thf(1605,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(730,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).

thf(2588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(846,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

thf(2850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(1484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(536,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(2160,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(566,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

thf(2224,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(1038,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(1869,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(660,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(2429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).

thf(1235,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(620,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).

thf(2337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(425,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

thf(1901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).

thf(1679,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
        = B )
      | ( ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__idI__1__1 ) ) @ ( A @ hAPP ) )
       != ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__idI__1__1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__idI_1) ).

thf(2044,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
        = B )
      | ( ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__idI__1__1 ) ) @ ( A @ hAPP ) )
       != ( C @ ( B @ ( A @ c_List_Osko__List__Xmap__idI__1__1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1432,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(538,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

thf(2165,plain,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Obeta ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(1300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(459,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(1980,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(522,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).

thf(2128,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

thf(1830,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(362,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1763,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(780,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).

thf(2701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(684,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(2486,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(33,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

thf(951,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(735,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

thf(2599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(869,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( B @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).

thf(2903,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( B @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(165,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1285,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(350,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) ) )
      = ( C @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

thf(1738,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) ) )
      = ( C @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(1358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(439,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(1934,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(715,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).

thf(2558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(379,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(1802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(640,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(2379,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(707,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(2543,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(899,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(2975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(725,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

thf(2579,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(789,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(2722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

thf(2030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(845,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rev_0) ).

thf(2848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(584,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(2266,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(659,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__1__class_Oof__nat__code_0) ).

thf(2426,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBC ) ) ) ) @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(907,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

thf(2992,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).

thf(1536,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(591,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).

thf(2279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(456,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(1972,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
        = C )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).

thf(1052,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
        = C )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(1506,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(1749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(1427,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(978,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(1140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(864,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

thf(2892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(416,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(1881,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(827,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

thf(2807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(878,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

thf(2924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(673,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

thf(2458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).

thf(2088,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(832,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).

thf(2818,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(1817,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(2611,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).

thf(1126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(857,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(2875,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(1940,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(432,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).

thf(1918,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(311,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).

thf(1649,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(627,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(2352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(13,axiom,
    tc_Int_Oint @ class_Divides_Oring__div,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).

thf(931,plain,
    tc_Int_Oint @ class_Divides_Oring__div,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(328,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

thf(1685,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(778,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(2696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(118,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).

thf(1157,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(501,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).

thf(2078,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(430,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(1913,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(562,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(2215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(258,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1517,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(909,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).

thf(2997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(548,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

thf(2187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping ) ) )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(208,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(1390,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(876,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(2919,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).

thf(2071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(812,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

thf(2775,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(1807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(871,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(2907,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(588,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(2273,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(323,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).

thf(1674,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(651,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

thf(2406,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(713,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

thf(2554,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).

thf(1481,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(2004,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(479,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(2026,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(897,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).

thf(2971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(739,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(2608,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( E @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).

thf(1646,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( E @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(666,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

thf(2443,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(905,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).

thf(2988,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1385,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(733,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

thf(2594,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

thf(2174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(644,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(2389,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(1341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(509,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

thf(2098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(847,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).

thf(2853,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(597,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).

thf(2290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(77,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1062,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(28,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(946,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(94,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(912,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(3003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(807,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(2764,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(1822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(1558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(882,axiom,
    tc_nat @ class_Divides_Osemiring__div,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

thf(2934,plain,
    tc_nat @ class_Divides_Osemiring__div,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(582,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).

thf(2262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(502,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(2081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(873,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

thf(2912,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(758,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(2648,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(176,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(1308,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(537,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

thf(2162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(295,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1607,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(1661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(519,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(2120,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(875,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).

thf(2917,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(476,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).

thf(2019,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(656,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(2421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(2009,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).

thf(1861,plain,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(66,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

thf(1030,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(891,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).

thf(2956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(680,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

thf(2475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(817,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(2786,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(11,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

thf(929,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(617,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(2330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).

thf(1893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(599,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(2294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(797,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

thf(2739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(229,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).

thf(2218,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(2102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).

thf(1774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(696,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(2517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

thf(1578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(642,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(2385,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(2233,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).

thf(1546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(698,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(2522,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(1876,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(262,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

thf(1248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

thf(1757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(638,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(2374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(1725,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(1280,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(32,axiom,
    tc_Int_Oint @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

thf(950,plain,
    tc_Int_Oint @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1097,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(729,axiom,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(2587,plain,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).

thf(1593,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(795,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(2736,plain,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(1303,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(1986,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

thf(1859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1,negated_conjecture,
    ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( v_i____ @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_u____ @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(918,plain,
    ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( v_i____ @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_u____ @ ( c_Lambda_Osubst @ c_COMBC ) ) ) ) @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ c_COMBC ) ) ) ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(250,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
        = ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
       != ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

thf(1495,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
        = ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
       != ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(800,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(2746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(721,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(2572,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).

thf(1789,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(634,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(2366,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(743,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

thf(2619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(766,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(2668,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(10,axiom,
    tc_Int_Oint @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

thf(928,plain,
    tc_Int_Oint @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(802,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).

thf(2751,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(823,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(2800,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(619,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

thf(2334,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(216,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

thf(1410,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(893,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

thf(2961,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1288,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(338,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
      | ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).

thf(1710,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
      | ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).

thf(2091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(650,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).

thf(2404,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(786,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(2714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

thf(1891,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(821,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).

thf(2795,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(1473,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(477,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

thf(2021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).

thf(1346,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(495,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

thf(2063,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(828,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
      | ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
      | ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).

thf(2810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
      | ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
      | ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(157,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( B
        = ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).

thf(1261,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
      | ( B
        = ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1019,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(727,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(2583,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(992,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).

thf(1500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(692,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oreplicate ) ) )
      = ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).

thf(2507,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_List_Oreplicate ) ) )
      = ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(1925,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(705,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
      = ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).

thf(2539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
      = ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(586,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(2270,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).

thf(1120,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
      = ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).

thf(1093,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
      = ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

thf(1930,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(690,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

thf(2502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(573,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

thf(2241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

thf(987,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(1977,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(825,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I1_J_0) ).

thf(2803,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_Olist__size ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(844,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(2847,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(774,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

thf(2687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(852,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(2864,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(415,axiom,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(1880,plain,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(917,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(3013,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(859,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).

thf(2879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(717,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

thf(2563,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(775,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(2690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(494,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(2059,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(626,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(2351,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(2655,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(2321,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(22,axiom,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).

thf(940,plain,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(17,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

thf(935,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(1945,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(1009,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(5,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).

thf(923,plain,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(349,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).

thf(1737,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(853,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Oshift ) ) ) )
      = ( D @ ( C @ ( B @ c_Suc @ ( D @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Oshift ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).

thf(2866,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Oshift ) ) ) )
      = ( D @ ( C @ ( B @ c_Suc @ ( D @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Oshift ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(838,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(2832,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(664,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

thf(2438,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(248,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ c_Type_Otype_OFun ) @ ( B @ ( A @ c_Type_Otyping ) ) )
      | ~ ( E @ ( C @ ( A @ c_Type_Otyping ) ) )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

thf(1490,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ c_Type_Otype_OFun ) @ ( B @ ( A @ c_Type_Otyping ) ) )
      | ~ ( E @ ( C @ ( A @ c_Type_Otyping ) ) )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(550,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(2191,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(810,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(2771,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(3018,plain,
    $false,
    inference(e,[status(thm)],[2452,2094,1024,2341,1840,2499,2480,1179,1295,2250,1036,2822,2630,1337,1718,2744,1369,2889,1190,2109,1454,1633,2778,2412,1237,2921,1031,2463,1899,2544,941,1956,1950,2395,1073,1728,1692,1305,1437,1486,2363,1855,1200,2309,2512,1005,2210,2940,1596,2231,2622,1522,2644,994,2527,2953,2590,1401,2947,1939,2248,2671,1544,2014,3012,1205,2282,1591,2114,2837,1142,1269,1655,2035,1735,2448,2141,1327,2627,1988,1761,945,2042,1458,2575,2195,1705,1867,2184,1164,2316,2434,2712,1222,930,2360,1095,2348,2432,1441,1046,1650,2886,1366,2531,2869,2548,1782,2491,1243,2985,2227,1391,1576,2400,1529,1904,1703,1623,1254,1628,1055,2603,2039,2339,1871,2708,1907,1264,1323,1511,1826,1455,2488,2466,949,2703,2698,1298,2897,934,1462,1132,1922,1800,1147,1890,1572,1398,1568,2520,2158,1641,2301,1963,2533,1232,2829,2169,1087,1514,2049,2552,2635,2929,2456,924,2616,1664,2324,2259,2650,2236,1334,1136,2122,1828,1677,2555,2073,2017,2178,2222,2950,1415,2105,1811,1911,2782,1109,2469,1151,937,1383,2254,1581,966,1843,2281,1896,1886,1796,2137,1351,1943,1600,2205,2884,1975,2762,981,2964,2437,1928,2861,1215,1447,2483,2371,2979,2002,998,2286,2639,1104,1697,2392,2154,1863,920,942,2204,2473,925,1153,2118,2047,1708,2737,2641,1311,2296,2307,1067,2496,2621,2660,1768,2905,2382,2773,2000,1636,1387,1091,1021,2277,1123,1666,2969,2937,1824,2132,2015,1274,2673,2705,2264,2409,1343,2560,2805,952,2541,1570,1174,1217,2147,1883,1560,1602,1920,2477,1968,1888,1687,2200,2179,1195,2344,1740,974,2958,1423,2332,2826,2820,2872,1951,2068,1819,1836,1787,2181,1079,2327,2112,1291,2769,1012,2653,1106,1936,1983,2840,1804,2895,1498,1878,1755,2268,2515,2100,1851,1772,1259,2946,2990,2377,948,2801,1534,1794,1017,1953,1375,2973,2577,1064,1970,1227,2694,1425,2509,1672,1138,2724,1719,2858,3001,989,1329,1361,1659,933,1182,2868,1584,1207,1644,1612,2798,1683,1160,2877,1028,1082,2023,2312,3010,2455,1700,2613,1791,2172,1155,1744,1114,1776,1478,2304,1539,2845,1668,2243,1060,2006,2566,1947,2813,1874,1715,2756,1525,2125,1099,2536,2681,1266,2900,2387,2355,1932,984,2505,2766,2052,1246,1759,1393,1202,1779,2208,1695,921,1563,2793,1996,1434,1857,1991,2788,1814,938,1241,2546,2057,1712,1846,2076,2748,1170,1286,2368,1466,2402,1187,2440,1026,1167,2645,2189,2995,953,2662,1185,2423,2529,926,2909,2144,2729,1251,2292,2585,1548,2602,1631,2677,2176,2275,2033,2149,2717,1219,2570,1747,2028,2734,1833,2727,1007,1916,2859,2791,2981,1620,1752,1652,1965,1520,2134,1615,1784,2525,2657,2674,2568,958,1403,1256,1488,1503,2193,936,2220,2326,1271,1865,1107,1332,1092,2425,1638,2935,1733,1239,1997,2759,2753,2166,1765,1090,1464,947,2573,2358,2319,1356,2346,2361,2679,1574,1542,2116,2943,1043,2856,1690,1439,2065,1853,1408,2151,2229,2084,2214,2624,2415,2493,2637,1117,990,996,2284,2257,1589,2246,1492,2299,1722,1144,2197,1307,2824,1471,2742,1993,2780,1731,2446,1293,2461,2710,1112,2812,2632,1339,2605,2314,2625,1909,1162,1838,1325,2593,3006,1149,964,1556,1460,2647,943,2252,2842,932,2418,1841,2365,2212,2835,2086,2139,1176,2303,2051,2550,2369,1015,2931,2288,1364,2967,2999,2156,922,2693,2984,1805,1076,2054,1809,2096,2107,2471,1420,1277,1134,2449,2927,939,2899,968,1551,2582,1049,1626,3009,1034,2239,2914,2816,944,2665,2318,2784,2271,927,2037,2684,2202,2597,1958,1598,1961,2397,1070,2977,1743,971,2732,1753,2720,1531,2882,1798,2298,1003,1770,1566,2012,1605,2588,2850,1484,2160,2224,1038,1869,2429,1235,2337,1901,1679,2044,1432,2165,1300,1452,1980,2128,1317,1830,1763,2701,2486,951,2599,2903,1285,1738,1358,1934,1849,2558,1802,2379,2543,2975,2579,1670,2722,2030,2848,2266,1617,2426,2992,1536,1353,2279,1972,1052,1506,1749,1427,978,1140,1372,2892,1881,2807,2924,2458,2088,2818,1817,976,1412,2611,1126,2875,1940,1918,1649,2352,1084,931,1685,2696,1553,1157,2078,1913,2215,1517,2997,2187,1390,2919,2071,2775,1807,2907,2273,1674,2406,2554,1481,2004,2026,2971,2608,2130,1646,2443,961,2988,1385,2594,2174,2389,1341,2098,2853,2290,1062,1508,946,1101,3003,2764,1822,1558,2934,2262,2081,2912,2648,1308,1193,2162,1212,1607,1661,2120,2917,2019,2421,2009,1861,1030,2956,2475,2786,929,2330,1893,2294,2739,1444,2218,2102,1774,2517,1578,2385,2233,1546,1395,2522,1876,1527,1248,1757,2374,1348,1725,1280,950,1097,2587,1593,1380,2736,1303,1986,1859,918,1314,1495,2746,2572,1789,2366,2619,2668,928,2751,2800,1657,2334,1172,1410,2961,1288,1710,1197,2091,2404,2714,1891,2795,1473,2021,1346,2063,1610,2810,1261,1378,1019,2583,992,1500,2507,1925,2539,2270,1120,1093,1930,2502,2241,987,1977,1129,2803,2847,2687,2864,1880,3013,2879,1320,2563,1681,2690,2059,2351,1468,2655,2321,940,935,1945,1009,923,1737,2866,2832,2438,1490,2191,1449,1417,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL805-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41  % Computer : n026.cluster.edu
% 0.15/0.41  % Model    : x86_64 x86_64
% 0.15/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41  % Memory   : 8046.5625MB
% 0.15/0.41  % OS       : Linux 6.8.0-71-generic
% 0.15/0.41  % CPULimit : 300
% 0.15/0.41  % WCLimit  : 300
% 0.15/0.41  % DateTime : Fri Sep 25 23:39:12 UTC 2026
% 0.15/0.42  % CPUTime  : 
% 0.15/0.42  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.91/1.38  % [INFO] 	 Parsing done (388ms). 
% 2.35/1.40  % [INFO] 	 Running in sequential loop mode. 
% 2.96/1.78  % [INFO] 	 eprover registered as external prover. 
% 2.96/1.78  % [INFO] 	 Scanning for conjecture ... 
% 3.46/2.00  % [INFO] 	 Found a conjecture (or negated_conjecture) and 918 axioms. Running axiom selection ... 
% 5.25/2.34  % [INFO] 	 Axiom selection finished. Selected 916 axioms (removed 2 axioms). 
% 6.59/2.67  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 6.59/2.69  % [INFO] 	 Type checking passed. 
% 7.02/2.70  % [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 ... 
% 21.02/6.10  % External prover 'e' found a proof!
% 21.02/6.10  % [INFO] 	 Killing All external provers ... 
% 21.02/6.11  % Time passed: 5547ms (effective reasoning time: 4701ms)
% 21.02/6.12  % Axioms used in derivation (916): clsarity_fun__Lattices_Olower__semilattice, cls_Suc__pred_0, cls_inf__sup__aci_I2_J_0, cls_not__one__less__zero_0, cls_less__iff__diff__less__0_0, cls_shift__commute_0, cls_add__0__left_0, cls_linorder__antisym__conv2_1, cls_append__eq__append__conv__if_3, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_concat_Oinduct_1, cls_dB_Osimps_I6_J_0, cls_take__eq__Nil_0, cls_listsum__map__filter_2, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_power__0_0, cls_listsp_Oinduct_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_subst__map_0, cls_length__filter__le_0, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_rev__swap_1, cls_add__is__1_1, cls_less__diff__iff_1, cls_zero__less__one_0, cls_of__nat__add_0, clsarity_Int__Oint__Int_Onumber, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_remove1_Osimps_I2_J_0, cls_le__diff__iff_0, cls_listrelp_OCons_0, cls_of__nat__0_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_order__less__le__trans_0, cls_list__update__overwrite_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_subst__eq_0, cls_le__diff__conv_1, cls_liftn_Osimps_I1_J_1, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_map__replicate_0, cls_append__self__conv_0, cls_dB_Osimps_I8_J_0, cls_one__is__add_4, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_drop__append_0, cls_zero__le__one_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_take__0_0, cls_diff__Suc__1_0, cls_eq__diff__iff_0, cls_map__cong_1, cls_replicate__empty_0, cls_power__inject__exp_0, cls_less__antisym_0, cls_le__iff__inf_1, cls_power__increasing_0, cls_of__nat__less__iff_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_add__increasing2_0, cls_listsp_Oinduct_3, cls_list_Oinject_0, clsarity_bool__Lattices_Olower__semilattice, cls_mod__by__0_0, cls_add__is__1_2, cls_linorder__neqE_0, cls_listsum_Osimps_I1_J_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_map_Oinduct_1, cls_liftn_Osimps_I2_J_0, cls_less__add__Suc2_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_Cons__eq__map__conv_3, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_listsp__infI_0, cls_take__Cons_H_0, clsarity_fun__Orderings_Oorder, cls_rotate__map_0, cls_diff__add__cancel_0, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_add__le__cancel__left_1, cls_distinct__filter_0, cls_uIT_0, cls_add__is__0_0, cls_not__Cons__self2_0, cls_le__inf__iff_1, cls_rev__is__rev__conv_0, cls_one__is__add_1, cls_appR_0, clsarity_nat__Orderings_Olinorder, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_list__update__append_1, cls_mod__add__left__eq_0, cls_less__Suc__eq_2, cls_not__less__eq_1, cls_remove1__filter__not_0, cls_nat__add__left__cancel__less_0, cls_of__nat__aux_Osimps_I2_J_0, cls_add__le__cancel__right_1, cls_take__add_0, cls_distinct__rev_1, cls_append__eq__append__conv__if_6, cls_add__leE_0, cls_filter__eq__ConsD_2, cls_order__less__trans_0, cls_self__append__conv_0, cls_mod__diff__eq_0, cls_list_Osimps_I5_J_0, cls_inf__left__commute_0, cls_add__left__cancel_0, cls_power__less__imp__less__exp_0, cls_head__Var__reduction_1, cls_listsp_ONil_0, cls_inf1E_1, cls_comm__monoid__add_Omult__1__right_0, cls_drop__0_0, cls_lift__subst__lt_0, cls_power__le__imp__le__exp_0, cls_list__update__nonempty_1, cls_power__one_0, cls_add__diff__assoc2_0, cls_power__gt1_0, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_add__nonpos__neg_0, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_comm__monoid__add_Omult__assoc_0, cls_substn_Osimps_I1_J_2, cls_of__nat__0__less__iff_0, cls_add__cancel__21_1, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_beta_0, cls_append__Cons_0, cls_le__0__eq_0, cls_listsum__append_0, cls_rotate__conv__mod_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_mod__add__self2_0, cls_subst__preserves__beta_0, cls_Abs_0, cls_add__nonneg__pos_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_gr0I_0, cls_lift__type_0, cls_inf__commute_0, cls_add__gr__0_0, cls_Nil__is__map__conv_0, cls_drop__map_0, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_drop__Cons__number__of_0, cls_length__map_0, cls_filter_Osimps_I2_J_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add, cls_lem0_0, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, cls_diff__diff__right_0, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_zero__less__double__add__iff__zero__less__single__add_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_diff__diff__cancel_0, cls_order__less__asym_0, cls_add__less__mono_0, cls_of__nat__le__iff_1, cls_nat__less__cases_0, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_diff__diff__left_0, cls_mod__by__1_0, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, clsarity_nat__Divides_Osemiring__div, cls_one__le__power_0, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_sorted_Osimps_I3_J_1, cls_add__le__mono_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_add__right__mono_0, cls_list_Osize_I4_J_0, cls_less__iff__diff__less__0_1, cls_mod__if_1, cls_append1__eq__conv_1, cls_listsum_Osimps_I2_J_0, cls_order__eq__refl_0, clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add, cls_filter__append_0, cls_subst__gt_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_eq__number__of_0, cls_substn__subst__n_0, cls_of__nat__le__iff_0, cls_linorder__antisym__conv2_0, cls_distinct_Osimps_I1_J_0, cls_shift__eq_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_length__greater__0__conv_1, cls_liftn__0_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_concat_Oinduct_0, cls_length__remdups__eq_0, cls_replicate__append__same_0, cls_foldl__absorb0_0, cls_rev_Osimps_I2_J_0, cls_add__Suc_0, cls_rev__map_0, cls_list__update__append1_0, cls_filter_Osimps_I1_J_0, cls_take__1__Cons_0, cls_drop__Suc__Cons_0, cls_rev__singleton__conv_0, cls_le__imp__diff__is__add_1, cls_dB_Osimps_I3_J_0, cls_list__update__beyond_0, cls_listsp_Ocases_0, cls_Suc__leI_0, cls_listsp_Oinducts_1, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_append__Nil2_0, cls_add__less__cancel__right_1, cls_listrelp_ONil_0, cls_rotate__rev_0, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_append__self__conv2_0, cls_lift__lift_0, cls_remdups__id__iff__distinct_0, cls_one__is__add_5, cls_list_Osize_I2_J_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_mod__add__cong_0, clsarity_Int__Oint__Int_Oring__char__0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_add__left__mono_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_ATP__Linkup_OCOMBC__def_0, cls_self__append__conv2_0, cls_distinct__map_0, cls_listsp_Ocases_2, cls_length__0__conv_0, cls_App__eq__foldl__conv_0, cls_remdups__eq__nil__iff_1, cls_Nitpick_Olist__size__simp_I1_J_0, cls_of__nat__0__le__iff_0, cls_sorted__drop_0, cls_sorted_Osimps_I3_J_2, cls_dB_Osimps_I4_J_0, cls_append__eq__append__conv__if_4, clsarity_Int__Oint__Ring__and__Field_Oordered__semidom, cls_rotate__is__Nil__conv_0, cls_distinct__append_0, cls_add__strict__left__mono_0, cls_mod__le__divisor_0, cls_power__0__Suc_0, cls_mod__Suc_0, cls_map__eq__Cons__conv_3, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_remove1_Oinduct_0, cls_type_Osimps_I2_J_1, cls_map__ext_1, cls_not__less__eq__eq_1, cls_self__append__conv2_1, clsarity_Int__Oint__Lattices_Olattice, cls_le__iff__diff__le__0_0, cls_rotate__rotate_0, cls_nat__diff__split_0, cls_Suc__diff__1_0, cls_of__nat__1_0, 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cls_substn_Osimps_I3_J_0, cls_diffs0__imp__equal_0, cls_list_Osize_I1_J_0, clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_class__ringb_Osubr0__iff_1, cls_shift__gt_0, cls_one__is__add_3, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_list_Osplit_1, cls_not__less0_0, cls_le__infE_1, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_expand__Suc_0, cls_inf__le1_0, cls_subst__Abs_0, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_inf__left__idem_0, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_foldl__Nil_0, cls_distinct__drop_0, cls_Suc__less__eq_0, cls_le__iff__diff__le__0_1, cls_lift_Osimps_I1_J_0, cls_zero__le__power_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_take__drop_0, cls_order__less__imp__le_0, cls_add__leE_1, cls_Suc__pred_H_0, cls_le__eqI_1, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_Suc__diff__le_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_power__increasing__iff_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_subst__Var_0, cls_list_Oinduct_0, clsarity_Int__Oint__Ring__and__Field_Osemiring__1, cls_add__gr__0_1, cls_le__infI2_0, cls_le__add1_0, cls_mod__if_0, cls_le__less__Suc__eq_1, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_eq__iff__diff__eq__0_0, cls_Abs__eq__apps__conv_1, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_lift__types_0, cls_diff__commute_0, cls_power__strict__increasing__iff_0, cls_drop__all_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, cls_drop__eq__Nil_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, cls_le__eq__less__or__eq_0, cls_substs__lemma_0, cls_list__update__code_I3_J_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_xt1_I7_J_0, cls_remdups__eq__nil__iff_0, cls_linorder__not__less_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_upd__conv__take__nth__drop_0, cls_rev__rev__ident_0, cls_add__le__cancel__left_0, cls_power__decreasing_0, cls_sorted_Osimps_I3_J_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_le__neq__implies__less_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_filter_Osimps_I2_J_1, cls_distinct_Oinduct_1, cls_empty__replicate_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_o__apply_0, clsarity_Int__Oint__OrderedGroup_Osemigroup__add, cls_mod__self_0, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_le__refl_0, cls_power__0__left_1, cls_mod__Suc__eq__Suc__mod_0, cls_add__le__cancel__right_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_le__number__of__eq__not__less_0, cls_list__update__nonempty_0, cls_add__diff__inverse_0, cls_power__mono_0, cls_o__assoc_0, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_not__less__eq__eq_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_semiring__1__class_Oof__nat__code_0, cls_inf1E_0
% 21.02/6.12  % No. of inferences in proof: 1835
% 21.02/6.12  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5547 ms resp. 4701 ms w/o parsing
% 22.45/6.39  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.91/6.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------