%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL816-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:32:01 EDT 2023

% Result   : Unsatisfiable 19.45s 6.44s
% Output   : Refutation 19.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  597
% Syntax   : Number of formulae    : 1102 ( 345 unt;  93 typ;   0 def)
%            Number of atoms       : 2179 ( 744 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 13394 (1142   ~;1170   |;   0   &;11082   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  150 ( 150   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   95 (  93 usr;  22 con; 0-6 aty)
%            Number of variables   : 2888 (   0   ^;2888   !;   0   ?;2888   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Type_Otyping_type,type,
    c_Type_Otyping: $i > $i > $i > $o ).

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

thf(v_e_____type,type,
    v_e____: $i ).

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

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

thf(c_List_Ofoldr_type,type,
    c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).

thf(c_Type_Otype_OFun_type,type,
    c_Type_Otype_OFun: $i ).

thf(v_Ts_____type,type,
    v_Ts____: $i ).

thf(v_T_H_____type,type,
    v_T_H____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_as_____type,type,
    v_as____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_ListOrder_Ostep1_type,type,
    c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).

thf(c_List_Olistsp_type,type,
    c_List_Olistsp: $i > $i > $i > $o ).

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

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

thf(class_Nat_Osemiring__char__0_type,type,
    class_Nat_Osemiring__char__0: $i > $o ).

thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

thf(c_Type_Otype_OAtom_type,type,
    c_Type_Otype_OAtom: $i > $i ).

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

thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

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

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

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

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

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

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

thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_type,type,
    c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

thf(v_T_____type,type,
    v_T____: $i ).

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

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

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

thf(v_T_H_H_____type,type,
    v_T_H_H____: $i ).

thf(c_Type_Osko__Type__Xtyping__elims__2__1_type,type,
    c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).

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

thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_type,type,
    c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xvar__app__types__1__1_type,type,
    c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).

thf(c_Lambda_Obeta_type,type,
    c_Lambda_Obeta: $i ).

thf(v_rs_____type,type,
    v_rs____: $i ).

thf(v_a_____type,type,
    v_a____: $i ).

thf(class_Ring__and__Field_Osemiring__1_type,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

thf(class_Ring__and__Field_Osemiring__0_type,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

thf(c_Type_Otype_Otype__case_type,type,
    c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).

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

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

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

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

thf(c_Type_Otype_Otype__rec_type,type,
    c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).

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

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

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

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

thf(c_Lambda_OdB_OdB__size_type,type,
    c_Lambda_OdB_OdB__size: $i > $i ).

thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_type,type,
    c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).

thf(c_OrderedGroup_Oab__semigroup__add_type,type,
    c_OrderedGroup_Oab__semigroup__add: $i > $i > $o ).

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

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

thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_type,type,
    c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).

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

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

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

thf(892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
      = ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(1322,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
      = ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(1337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(391,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
      | ~ ( c_Type_Otypings @ A @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).

thf(1411,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
      | ~ ( c_Type_Otypings @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(1633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(1315,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(1083,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(941,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
      = ( c_Lambda_OdB_OAbs @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

thf(1179,plain,
    ! [A: $i] :
      ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
      = ( c_Lambda_OdB_OAbs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(1549,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(468,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ D ) @ B ) @ E )
      | ~ ( c_Type_Otyping @ A @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

thf(1586,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ D ) @ B ) @ E )
      | ~ ( c_Type_Otyping @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).

thf(1501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(809,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(1024,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(373,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).

thf(1369,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(1168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(102,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
      | ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).

thf(760,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
      | ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(222,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
      = ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).

thf(1031,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
      = ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(454,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

thf(1554,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(1110,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(297,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1200,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(683,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(1522,plain,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(482,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

thf(1618,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(397,axiom,
    c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_H_0) ).

thf(1422,plain,
    c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).

thf(741,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(1205,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(470,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(1591,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(329,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1269,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(878,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

thf(1158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

thf(582,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(428,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).

thf(1497,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(241,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(1078,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(499,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
      = ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).

thf(1655,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
      = ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1137,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(347,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

thf(1310,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

thf(715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(332,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

thf(1275,plain,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(913,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(492,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(1640,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(309,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(1222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(1001,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

thf(1243,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( C
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( C
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldr @ A @ B @ C @ D @ D )
        = ( c_List_Ofoldl @ A @ C @ B @ D @ D ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add_Ofoldr__conv__foldl_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldr @ A @ B @ C @ D @ D )
        = ( c_List_Ofoldl @ A @ C @ B @ D @ D ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(1601,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ A ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).

thf(1095,plain,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ A ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(157,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_varT_0) ).

thf(885,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(1046,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
     != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

thf(1482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
     != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(323,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(1254,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1287,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(401,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(1430,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(501,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(1660,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(112,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( C = B )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).

thf(785,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( C = B )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
      | ~ ( c_List_Olistsp @ c_InductTermi_OIT @ A @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).

thf(1511,plain,
    ! [A: $i] :
      ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
      | ~ ( c_List_Olistsp @ c_InductTermi_OIT @ A @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(119,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(802,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

thf(934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(414,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(1462,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(542,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(125,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(817,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(478,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_Lambda_OdB_OAbs @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(606,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_Lambda_OdB_OAbs @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(1013,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(1641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(1494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(504,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(1664,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(395,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(1418,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(466,axiom,
    ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(1581,plain,
    ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(336,axiom,
    c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).

thf(1283,plain,
    c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(1051,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(1072,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(660,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(203,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(988,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(1433,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

thf(1405,plain,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

thf(1201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(252,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(1104,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(507,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(153,axiom,
    ! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

thf(877,plain,
    ! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ D @ C @ A ) )
      | ( B = D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(1622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ D @ C @ A ) )
      | ( B = D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(476,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

thf(1604,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

thf(920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

thf(1153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(1067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(82,axiom,
    ! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

thf(714,plain,
    ! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(1636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

thf(798,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(1163,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1387,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( C
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

thf(1343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( C
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1355,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(1255,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(862,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
       != ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
      | ( B = D )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

thf(1570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
       != ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
      | ( B = D )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(306,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(1217,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(126,axiom,
    c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(820,plain,
    c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OVar @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(1487,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OVar @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(630,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(457,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( v_T____
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
      | ~ ( c_Type_Otyping @ F @ D @ B )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).

thf(1560,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( v_T____
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
      | ~ ( c_Type_Otyping @ F @ D @ B )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).

thf(957,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

thf(894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(483,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(1619,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(398,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(1423,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(171,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).

thf(916,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).

thf(566,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ B @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ B @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(665,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(1457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

thf(889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ A ) @ tc_Lambda_OdB )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).

thf(1210,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ A ) @ tc_Lambda_OdB )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
     != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

thf(1407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
     != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1392,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__ac_I1_J_0) ).

thf(1291,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

thf(1106,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(462,axiom,
    c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).

thf(1573,plain,
    c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
      | ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

thf(974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
      | ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

thf(1402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(1143,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1534,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(1328,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1121,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

thf(1064,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(1227,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(429,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(1498,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(1425,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

thf(1006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(593,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(869,plain,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(42,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = D )
      | ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).

thf(610,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = D )
      | ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(783,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(989,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(1592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

thf(697,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Lambda_OdB_OdB__size @ B ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).

thf(1234,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Lambda_OdB_OdB__size @ B ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(448,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_0) ).

thf(1541,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
     != ( c_Type_Otype_OAtom @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).

thf(1397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
     != ( c_Type_Otype_OAtom @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(460,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(1567,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(277,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(1160,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( c_Lambda_OdB_OAbs @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( c_Lambda_OdB_OAbs @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(1361,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(179,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(933,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(1182,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(642,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).

thf(637,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(305,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1214,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(301,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1207,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(494,axiom,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(1644,plain,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(1155,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).

thf(901,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(1075,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(342,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(1297,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(1552,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(1192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(1060,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(47,axiom,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(622,plain,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(353,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(1324,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
        = ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__commute_0) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
        = ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(57,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).

thf(647,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(1263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(208,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).

thf(997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(469,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(1099,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(515,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(1150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1266,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1231,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(264,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(1131,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(60,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = D )
      | ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).

thf(654,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = D )
      | ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(201,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(984,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(169,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Otyping @ A @ B @ C )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
      | ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

thf(911,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Otyping @ A @ B @ C )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
      | ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(474,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
      = ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).

thf(1599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
      = ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
      | ~ ( c_Type_Otyping @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

thf(1246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
      | ~ ( c_Type_Otyping @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(486,axiom,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(1627,plain,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(1525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1333,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(1318,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(317,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

thf(1241,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1170,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(1026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(530,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(926,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(244,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ tc_Lambda_OdB )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ B @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).

thf(1086,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ tc_Lambda_OdB )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ B @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(458,axiom,
    ! [A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(1563,plain,
    ! [A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
     != ( c_Lambda_OdB_OAbs @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(1466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
     != ( c_Lambda_OdB_OAbs @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(1187,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(674,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

thf(794,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(159,axiom,
    class_Power_Opower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(888,plain,
    class_Power_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ C ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(906,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ C ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

thf(1278,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

thf(1135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

thf(1146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(128,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
      = ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).

thf(824,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
      = ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(451,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(1548,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

thf(745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

thf(573,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(1374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(750,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(488,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_COMBB @ A @ B @ C @ D @ E @ F )
      = ( hAPP @ A @ ( hAPP @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

thf(1631,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_COMBB @ A @ B @ C @ D @ E @ F )
      = ( hAPP @ A @ ( hAPP @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(733,plain,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(562,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_Lambda_OdB_OAbs @ C ) )
      | ( A
        = ( c_Lambda_OdB_OAbs @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

thf(1652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_Lambda_OdB_OAbs @ C ) )
      | ( A
        = ( c_Lambda_OdB_OAbs @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
      = ( hAPP @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).

thf(1520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
      = ( hAPP @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(1124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(545,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(1615,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(152,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(875,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

thf(826,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(1428,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(1139,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

thf(936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(348,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(357,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1332,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

thf(1090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).

thf(1464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(1194,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

thf(831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(258,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).

thf(1117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(229,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

thf(1048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(1349,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1492,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
        = ( c_Lambda_OdB_OVar @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1175,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(463,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(1574,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(155,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
        = ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).

thf(880,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
        = ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_OAtom @ A )
     != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).

thf(1043,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_OAtom @ A )
     != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ B @ C )
      | ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ B @ C )
      | ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
      = ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).

thf(1376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
      = ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(811,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(418,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(1471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(192,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(964,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

thf(1022,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).

thf(1112,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(278,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).

thf(1162,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(848,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

thf(520,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(1556,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(1460,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(286,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
     != ( c_Lambda_OdB_OVar @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(1381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
     != ( c_Lambda_OdB_OVar @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(1474,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

thf(1594,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(959,plain,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D )
      | ~ ( c_List_Olistsp @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

thf(695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D )
      | ~ ( c_List_Olistsp @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(1,negated_conjecture,
    ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(505,plain,
    ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(174,axiom,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(922,plain,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(407,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
      | ( ( c_Suc @ A )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
      | ( ( c_Suc @ A )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(443,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

thf(1528,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(851,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(251,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ B ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
      | ~ ( c_Type_Otypings @ ( c_Type_Oshift @ A @ C @ F @ tc_Type_Otype ) @ D @ E )
      | ~ ( c_Type_Otyping @ A @ B @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).

thf(1102,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ B ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
      | ~ ( c_Type_Otypings @ ( c_Type_Oshift @ A @ C @ F @ tc_Type_Otype ) @ D @ E )
      | ~ ( c_Type_Otyping @ A @ B @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(392,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(1413,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(467,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(1583,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(503,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).

thf(1662,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(281,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(1166,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

thf(944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(396,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(1420,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(1509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(242,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(1081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(361,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(1340,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(1018,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Otype_OAtom @ A )
       != ( c_Type_Otype_OAtom @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).

thf(754,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Otype_OAtom @ A )
       != ( c_Type_Otype_OAtom @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(553,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(288,axiom,
    class_Nat_Osemiring__char__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(1181,plain,
    class_Nat_Osemiring__char__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(134,axiom,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(836,plain,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(1208,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

thf(580,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(151,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

thf(872,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(479,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(1611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(386,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

thf(1400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Oliftn @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
      = ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ C ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).

thf(1647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ C ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(372,axiom,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(1368,plain,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(444,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

thf(1531,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(206,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
      = ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(993,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
      = ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1003,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

thf(1300,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(291,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1186,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(1038,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

thf(1538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(465,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

thf(1579,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(1218,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(308,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

thf(1220,plain,
    v_n____ = v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(1053,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(430,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1499,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(368,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1358,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(43,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

thf(613,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
        = ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
        = ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(147,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( v_T____
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
      | ~ ( c_Type_Otyping @ F @ D @ A )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).

thf(864,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( v_T____
       != ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
      | ~ ( c_Type_Otyping @ F @ D @ A )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(432,axiom,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

thf(1504,plain,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(978,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

thf(571,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(269,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ F @ E @ G )
      = ( c_List_Ofoldr @ ( c_Fun_Ocomp @ A @ B @ E @ ( tc_fun @ G @ G ) @ D ) @ C @ F @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__map_0) ).

thf(1141,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ F @ E @ G )
      = ( c_List_Ofoldr @ ( c_Fun_Ocomp @ A @ B @ E @ ( tc_fun @ G @ G ) @ D ) @ C @ F @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(1372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(595,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

thf(556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(178,axiom,
    ( v_rs____
    = ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).

thf(931,plain,
    ( v_rs____
    = ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1448,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(1108,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(198,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
      | ~ ( c_Type_Otyping @ A @ C @ E )
      | ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

thf(976,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
      | ~ ( c_Type_Otyping @ A @ C @ E )
      | ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(903,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(1289,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(1276,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
      = ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).

thf(1326,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
      = ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(699,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ A ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).

thf(1062,plain,
    ! [A: $i] :
      ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ A ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(487,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ B @ C @ D @ E )
      = ( c_List_Ofoldl @ ( c_COMBC @ A @ D @ E @ E ) @ C @ ( c_List_Orev @ B @ D ) @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).

thf(1629,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldr @ A @ B @ C @ D @ E )
      = ( c_List_Ofoldl @ ( c_COMBC @ A @ D @ E @ E ) @ C @ ( c_List_Orev @ B @ D ) @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(961,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_Lambda_OdB_OVar @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_Lambda_OdB_OVar @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(456,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
      | ~ ( c_Type_Otypings @ A @ F @ G )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

thf(1558,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
      | ~ ( c_Type_Otypings @ A @ F @ G )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OAbs @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(1294,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OAbs @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(103,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
      | ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).

thf(763,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
      | ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(1513,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(406,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(1444,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(899,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(502,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(1661,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(480,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1614,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(800,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

thf(1133,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
      | ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(99,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
      | ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).

thf(752,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
      | ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(1280,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(312,axiom,
    ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(1229,plain,
    ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(1546,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(378,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1380,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(1248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(1480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(92,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(735,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) @ D )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ C ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).

thf(999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) @ D )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ C ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(620,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(967,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(249,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1097,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(133,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(835,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(485,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

thf(1625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(854,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(344,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).

thf(1303,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(442,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).

thf(1527,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ A @ B @ C )
      = ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).

thf(1148,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubstn @ A @ B @ C )
      = ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1436,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(172,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Omap @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).

thf(918,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Omap @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(370,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).

thf(1363,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(500,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( B = C )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).

thf(1657,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( B = C )
      | ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ B @ C )
      | ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).

thf(807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olistsp @ A @ B @ C )
      | ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1335,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

thf(635,plain,
    ! [A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(280,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1165,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_1) ).

thf(955,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(363,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

thf(1346,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(158,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(886,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(1172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(897,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(390,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1410,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ A ) @ tc_Lambda_OdB )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).

thf(1033,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ A ) @ tc_Lambda_OdB )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(296,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__left__commute_0) ).

thf(1197,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__add @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_Lambda_OdB_OAbs @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

thf(1352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_Lambda_OdB_OAbs @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(263,axiom,
    ( v_T____
    = ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).

thf(1129,plain,
    ( v_T____
    = ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

thf(1261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Orev @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

thf(575,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Orev @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(860,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

thf(1384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(377,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1378,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(528,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(367,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1357,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

thf(908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(141,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(850,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(1597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(150,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(871,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

thf(1093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
      | ~ ( c_Type_Otypings @ A @ C @ E )
      | ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

thf(839,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
      | ~ ( c_Type_Otypings @ A @ C @ E )
      | ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(477,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( c_Lambda_OdB_OVar @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( c_Lambda_OdB_OVar @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1320,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(1009,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(175,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ B @ A @ C @ D ) @ B @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A )
      | ~ ( c_Type_Otypings @ C @ F @ G )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

thf(923,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ B @ A @ C @ D ) @ B @ tc_Type_Otype @ tc_Type_Otype ) )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A )
      | ~ ( c_Type_Otypings @ C @ F @ G )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(290,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
      = ( hAPP @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
      = ( hAPP @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1416,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(245,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ C @ D @ E )
      = ( c_List_Ofoldr @ ( c_COMBC @ A @ D @ E @ D ) @ ( c_List_Orev @ C @ E ) @ B @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).

thf(1088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ofoldl @ A @ B @ C @ D @ E )
      = ( c_List_Ofoldr @ ( c_COMBC @ A @ D @ E @ D ) @ ( c_List_Orev @ C @ E ) @ B @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(238,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

thf(1069,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
      | ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(708,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(972,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(1490,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(775,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

thf(560,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(1980,plain,
    $false,
    inference(cvc4,[status(thm)],[892,1322,1337,1411,1633,846,1315,1083,941,1179,1549,1586,1501,809,1024,1469,1369,1190,1168,760,628,1031,1554,1110,1200,683,730,1522,1618,1422,741,1205,1591,1269,878,677,1041,523,1158,582,1305,597,1497,1078,1655,1137,1310,715,1275,913,1640,1222,1001,1243,1576,1441,841,1645,1601,829,1095,885,1046,1482,1254,724,1287,1430,1660,719,785,1330,1511,802,1455,934,1462,542,817,1609,606,1013,1641,1494,1664,1418,1581,1283,1051,821,981,687,1072,660,988,1433,1405,1201,1104,507,877,692,1119,1622,1604,920,512,1153,534,1067,714,1636,798,1163,1387,1343,778,952,1355,1255,862,1570,1217,820,1487,630,1560,957,894,788,1619,1423,916,566,1365,625,665,1457,889,1210,1407,551,1392,1291,1106,1573,974,1402,1143,1270,1534,615,1328,1121,1064,1227,1498,1425,1006,593,869,610,783,989,1592,578,697,1234,1541,857,1397,1567,1160,1028,1361,933,1182,642,637,1214,1207,1644,970,1155,706,901,1075,1414,526,701,1297,1451,1552,1192,1060,622,837,1324,1114,647,1263,997,1588,1099,985,515,1150,1266,1231,1131,654,984,911,1599,1246,1627,1525,1333,1318,1241,805,765,1170,1035,1515,1026,530,926,1086,938,1563,657,1466,558,1187,674,794,586,662,888,906,1278,1135,618,1146,824,1548,745,573,689,1374,601,965,750,1631,733,562,772,1652,743,1520,1124,545,1615,1389,875,826,1428,1139,936,1312,1058,1239,1332,1090,1258,540,1464,947,1638,1224,604,1194,831,1117,1048,1349,1492,1307,1175,1574,1011,880,649,1043,599,1376,1439,811,1471,758,964,1022,668,1112,1162,726,848,520,1556,769,1460,1177,1381,1474,1594,959,695,780,883,1015,1477,1250,505,922,1445,1528,851,1102,1413,722,1583,1662,1166,944,680,548,1420,1509,1081,1340,1018,754,553,1181,836,1203,1208,589,580,872,1611,1400,1647,1252,739,1368,1531,993,712,1003,1300,791,1186,1038,717,1538,1579,1218,1220,1053,1499,1358,1543,703,613,1284,864,1504,978,571,1272,991,1141,1536,1485,1506,1372,595,1649,556,931,671,1517,1126,1448,1108,976,903,1289,844,1453,1276,1326,699,517,748,1062,652,1629,632,961,813,995,1558,568,510,1294,929,1212,763,1513,1444,536,899,1661,1614,800,1133,752,1280,1229,1546,1380,1248,867,1480,735,999,620,833,967,950,1097,835,1395,1625,854,1303,1527,1148,564,1436,918,1363,1657,807,1335,1056,635,1165,955,1346,796,886,1172,897,1410,767,1033,1197,728,1236,1352,1129,1261,575,860,1384,1378,528,644,1357,908,850,1597,871,1093,839,1606,1320,1009,923,1184,1565,1416,639,1088,1069,708,972,1490,775,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : LCL816-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.17  % Command  : run_Leo-III %s %d
% 0.16/0.39  % Computer : n021.cluster.edu
% 0.16/0.39  % Model    : x86_64 x86_64
% 0.16/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39  % Memory   : 8042.1875MB
% 0.16/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39  % CPULimit : 300
% 0.16/0.39  % WCLimit  : 300
% 0.16/0.39  % DateTime : Thu May 18 16:06:13 EDT 2023
% 0.16/0.39  % CPUTime  : 
% 1.01/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.62/1.24  % [INFO] 	 Parsing done (270ms). 
% 1.87/1.25  % [INFO] 	 Running in sequential loop mode. 
% 2.29/1.53  % [INFO] 	 eprover registered as external prover. 
% 2.29/1.54  % [INFO] 	 cvc4 registered as external prover. 
% 2.29/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.71/1.67  % [INFO] 	 Found a conjecture and 505 axioms. Running axiom selection ... 
% 3.12/1.80  % [INFO] 	 Axiom selection finished. Selected 503 axioms (removed 2 axioms). 
% 3.84/1.94  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.84/1.95  % [INFO] 	 Type checking passed. 
% 3.84/1.96  % [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 ... 
% 19.45/6.43  % External prover 'cvc4' found a proof!
% 19.45/6.44  % [INFO] 	 Killing All external provers ... 
% 19.45/6.44  % Time passed: 5882ms (effective reasoning time: 5176ms)
% 19.45/6.44  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.45/6.44  % Axioms used in derivation (503): cls_type_Orecs_I2_J_0, cls_not__one__less__zero_0, cls_shift__commute_0, cls_add__0__left_0, cls_MI1_0, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, cls_subst__map_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_rev__swap_1, cls_add__is__1_1, cls_zero__less__one_0, cls_of__nat__add_0, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_of__nat__0_0, cls_subst__eq_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_order__eq__iff_0, cls_Cons__step1__Cons_0, cls_liftn_Osimps_I1_J_1, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_append__self__conv_0, cls_dB_Osimps_I8_J_0, cls_one__is__add_4, cls_ab__semigroup__add_Oadd__commute_0, cls_zero__le__one_0, cls_type_Osimps_I3_J_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_append__step1I_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_less__antisym_0, cls_liftn_Osimps_I2_J_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_var__app__typesE_0, cls_Cons__eq__map__conv_3, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_uT_H_0, cls_of__nat__less__iff_0, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_MI2_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_add__le__cancel__left_1, cls_uIT_0, cls_Snoc__step1__SnocD_2, cls_add__is__0_0, cls_not__Cons__self2_0, cls_less__Suc__eq_2, cls_type_Osimps_I4_J_0, cls_not__less__eq_1, cls_nat__add__left__cancel__less_0, cls_rev__is__rev__conv_0, cls_one__is__add_1, cls_add__le__cancel__right_1, clsarity_nat__Orderings_Olinorder, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_comm__monoid__add_Omult__1__right_0, cls_power__one_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_Cons__step1__Cons_5, cls_type_Osplit__asm_1, cls_add__left__cancel_0, cls_power__less__imp__less__exp_0, cls_head__Var__reduction_1, cls_power__gt1_0, cls_append__eq__Cons__conv_4, cls_add__nonpos__neg_0, cls_eq__Nil__appendI_0, 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_beta_0, cls_append__Cons_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_Abs_0, cls_foldl__foldr1_0, cls_add__nonneg__pos_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_gr0I_0, cls_lift__type_0, cls_add__gr__0_0, cls_Nil__is__map__conv_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_add__right__mono_0, cls_add__less__mono_0, cls_append1__eq__conv_1, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_headT_0, cls_order__eq__refl_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_substn__subst__n_0, cls_linorder__antisym__conv2_0, cls_foldl__foldr_0, cls_double__eq__0__iff_1, cls_shift__eq_0, cls_linorder__antisym__conv1_0, cls_liftn__0_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_dB_Osimps_I3_J_0, cls_foldl__absorb0_0, cls_rev_Osimps_I2_J_0, cls_add__Suc_0, cls_rev__map_0, cls_subst__Var_2, cls_rev__singleton__conv_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_append__Nil2_0, cls_add__less__cancel__right_1, cls_nat__add__left__commute_0, cls_append__self__conv2_0, cls_one__is__add_5, cls_class__semiring_Osemiring__rules_I6_J_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_Cons_0, cls_less__le__not__le_2, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_Nil__is__append__conv_0, cls_add__left__mono_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_typing__elims_I2_J_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_ATP__Linkup_OCOMBC__def_0, cls_self__append__conv2_0, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_power__0__Suc_0, cls_App__eq__foldl__conv_0, cls_of__nat__0__le__iff_0, cls_self__append__conv2_1, cls_dB_Osimps_I4_J_0, cls_Cons__step1__Cons_1, cls_map__eq__Cons__conv_3, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_type_Osimps_I5_J_0, cls_type_Osimps_I2_J_1, cls_typing__elims_I1_J_0, cls_append__is__Nil__conv_2, cls_Suc__neq__Zero_0, cls_map__is__Nil__conv_0, cls_append__eq__append__conv2_5, cls_var__app__types_0, cls_Cons__step1__Cons_3, cls_singleton__rev__conv_0, cls_append__eq__Cons__conv_5, cls_list__app__typeD_1, cls_append__in__listsp__conv_1, cls_add__is__1_0, cls_var__app__typesE_1, cls_power__eq__0__iff_2, cls_append__Nil_0, cls_class__semiring_Oadd__a_0, cls_append__in__listsp__conv_0, cls_dB_Osize_I5_J_0, cls_one__is__add_0, cls_less__add__Suc1_0, cls_Var__IT_0, cls_xt1_I8_J_0, cls_apps__preserves__betas_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_rev__is__Nil__conv_0, cls_of__nat__eq__iff_0, cls_Snoc__step1__SnocD_3, cls_argT_0, cls_comm__monoid__add_Omult__commute_0, cls_foldl__Cons_0, cls_add__right__cancel_0, cls_App_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_nT_0, cls_power__strict__mono_0, cls_zero__less__two_0, cls_True_0, cls_head__Var__reduction_0, cls_of__nat__0__less__iff_1, cls_lessI_0, cls_power__strict__decreasing_0, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_less__add__one_0, cls_not__leE_0, cls_ATP__Linkup_OCOMBB__def_0, cls_add__strict__mono_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_zero__less__power_0, cls_Abs__App__neq__Var__apps_0, cls_order__antisym_0, cls_order__trans_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_uT_0, cls_less__add__eq__less_0, cls_append__step1I_1, cls_type_Osplit_0, cls_not__Cons__self_0, cls_dB_Osimps_I1_J_0, cls_self__append__conv_1, cls_apps__eq__Abs__conv_2, cls_lift__map_0, cls_add__cancel__21_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_linorder__antisym__conv1_1, cls_dB_Osize_I3_J_0, cls_subst__Var_1, cls_Cons__step1__Cons_2, cls_Nil__is__append__conv_1, cls_varT_0, cls_type_Orecs_I1_J_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_type_Osimps_I1_J_0, cls_append__same__eq_0, cls_natgb_Oadd__cancel_0, cls_neq__Nil__conv_1, cls_type_Osimps_I2_J_0, cls_zero__neq__one_0, cls_neq0__conv_1, cls_linorder__not__le_1, cls_append__assoc_0, cls_not__Nil__step1_0, cls_apps__eq__Abs__conv_1, cls_dB_Osize_I4_J_0, cls_add__less__cancel__right_0, cls_type_Osplit_1, cls_foldr_Osimps_I2_J_0, cls_one__is__add_2, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, cls_lifts__IT_0, clsarity_nat__Orderings_Opreorder, cls_not__less__iff__gr__or__eq_1, cls_order__le__neq__trans_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_foldl__assoc_0, cls_map__map_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_order__eq__iff_2, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_append__in__listsp__conv_2, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_foldr__foldl_0, cls_foldl__foldr1__lemma_0, cls_Cons__step1__Cons_4, cls_linorder__neqE__ordered__idom_0, cls_map__append_0, cls_o__eq__dest_0, cls_dB_Osimps_I2_J_1, cls_var__app__types_1, cls_add__nonneg__nonneg_0, cls_o__eq__dest__lhs_0, cls_class__ringb_Oadd__r0__iff_0, cls_order__antisym__conv_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_foldr__append_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_foldr__map_0, cls_nat_Oinject_0, cls_add__strict__increasing_0, cls_rev__eq__Cons__iff_1, cls_power__strict__increasing__iff_1, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_Nat_Oadd__0__right_0, cls_liftn__lift_0, cls_map__is__Nil__conv_1, cls_power__le__imp__le__base_0, cls_list__app__typeD_0, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_Suc__lessD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_trans__less__add2_0, cls_add__is__1_4, cls_add__is__1_5, cls_xt1_I11_J_0, cls_map_Osimps_I2_J_0, cls_add__neg__neg_0, cls_dB_Osize_I1_J_0, cls_rev__is__Nil__conv_1, cls_natgb_Oadd__r0__iff_0, cls_ab__semigroup__add_Oadd__left__commute_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_abs_0, cls_less__Suc0_0, cls_Snoc__step1__SnocD_0, cls_Abs__eq__apps__conv_2, cls_xt1_I6_J_0, cls_le__add__right__mono_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_typing_OVar_0, cls_lift__IT_0, cls_IT_OVar_0, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_append__is__Nil__conv_1, cls_list__app__typeE_1, cls_double__add__less__zero__iff__single__less__zero_1, cls_typing__elims_I2_J_1, cls_nat_Osimps_I3_J_0, cls_plus__nat_Oadd__0_0, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_list__app__typeI_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_less__trans__Suc_0, cls_Nil__is__rev__conv_0, cls_comm__monoid__add_Omult__1_0, cls_liftn_Osimps_I1_J_0, cls_order__less__irrefl_0, cls_append__is__Nil__conv_0, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_append__eq__appendI_0, cls_list_Oinject_1, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_nat__add__left__cancel_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_apps__preserves__beta_0, cls_comp__cong_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_App__eq__foldl__conv_4, cls_Abs__eq__apps__conv_0, cls_singleton__rev__conv_1, cls_foldr__conv__foldl_0, cls_add__is__1_3, cls_foldl__append_0, cls_substn_Osimps_I1_J_1, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_power__inject__base_0, cls_less__SucI_0, cls_add__neg__nonpos_0, cls_not__less0_0, cls_dB_Osimps_I5_J_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_add__less__cancel__left_0, cls_subst__Var__IT_0, 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_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_foldl__Nil_0, cls_Suc__less__eq_0, cls_list__app__typeE_0, cls_lift_Osimps_I1_J_0, cls_zero__le__power_0, cls_rev__eq__Cons__iff_0, cls_ab__semigroup__add_Oadd__ac_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_order__less__imp__le_0, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_add__gr__0_2, cls_type_Osplit__asm_0, cls_add__less__le__mono_0, cls_add__gr__0_1, cls_power__strict__increasing__iff_0, cls_add__strict__increasing2_0, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_of__nat__Suc_0, cls_substs__lemma_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_dB_Osize_I6_J_0, cls_Abs__eq__apps__conv_1, cls_ab__semigroup__add_Ofoldr__conv__foldl_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_lift__types_0, cls_dB_Osize_I2_J_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_xt1_I7_J_0, cls_T_0, cls_linorder__not__less_1, cls_not__one__le__zero_0, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_rev__rev__ident_0, cls_add__le__cancel__left_0, cls_list_Osimps_I2_J_0, cls_Snoc__step1__SnocD_1, cls_zero__less__Suc_0, cls_append1__eq__conv_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_o__apply_0, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_even__less__0__iff_0, cls_power__0__left_1, cls_add__le__cancel__right_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_argsT_0, cls_power__mono_0, cls_o__assoc_0, cls_of__nat__less__0__iff_0, cls_type_Osimps_I6_J_0, cls_Abs__apps__eq__Abs__apps__conv_0
% 19.45/6.44  % No. of inferences in proof: 1009
% 19.45/6.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5882 ms resp. 5176 ms w/o parsing
% 19.68/6.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.68/6.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------