%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 11:32:19 EDT 2023

% Result   : Unsatisfiable 11.74s 3.59s
% Output   : Refutation 12.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  817
% Syntax   : Number of formulae    : 1539 ( 485 unt;  96 typ;   0 def)
%            Number of atoms       : 3087 (1044 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 18074 (1538   ~;1644   |;   0   &;14892   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  164 ( 164   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  96 usr;  13 con; 0-5 aty)
%            Number of variables   : 4044 (   0   ^;4044   !;   0   ?;4044   :)

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

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

thf(c_InductTermi_OIT_type,type,
    c_InductTermi_OIT: $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_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

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

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

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

thf(v_ta_____type,type,
    v_ta____: $i ).

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

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

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

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

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

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

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

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

thf(class_Int_Oring__char__0_type,type,
    class_Int_Oring__char__0: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_List_Onth_type,type,
    c_List_Onth: $i > $i > $i > $i ).

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

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

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

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

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

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

thf(class_Ring__and__Field_Oring__1_type,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

thf(c_List_Osublist_type,type,
    c_List_Osublist: $i > $i > $i > $i ).

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

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

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

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(tc_bool_type,type,
    tc_bool: $i ).

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

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

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

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

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

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

thf(v_s_____type,type,
    v_s____: $i ).

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

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

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

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

thf(c_Lambda_OdB_OdB__case_type,type,
    c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1_type,type,
    c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1: $i > $i > $i > $i > $i ).

thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_type,type,
    c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

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(637,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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__le__iff_0) ).

thf(2163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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)],[637]) ).

thf(147,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
        = ( c_List_Onth @ A @ E @ D ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).

thf(1036,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
        = ( c_List_Onth @ A @ E @ D ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(141,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(1024,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(296,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(1369,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)],[296]) ).

thf(624,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(2131,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)],[624]) ).

thf(411,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(1633,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(471,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(1767,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)],[471]) ).

thf(679,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(2263,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)],[679]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(1237,plain,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(87,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(893,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)],[87]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(1179,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(40,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(777,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)],[40]) ).

thf(551,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(1956,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)],[551]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_1) ).

thf(1586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(351,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(1501,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)],[351]) ).

thf(52,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(809,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)],[52]) ).

thf(608,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(2094,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)],[608]) ).

thf(313,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(1411,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)],[313]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
        = A )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).

thf(1168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
        = A )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(692,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_5) ).

thf(2295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(710,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(2341,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Orev @ A @ B ) @ C @ B )
        = ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Suc @ C ) @ tc_nat ) @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__nth_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Orev @ A @ B ) @ C @ B )
        = ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Suc @ C ) @ tc_nat ) @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(144,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(1031,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)],[144]) ).

thf(273,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(1315,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(505,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(1850,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)],[505]) ).

thf(167,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(1083,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)],[167]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(563,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(1982,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)],[563]) ).

thf(686,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).

thf(2280,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).

thf(1554,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(434,axiom,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(1686,plain,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(674,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(2250,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)],[674]) ).

thf(225,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(1211,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)],[225]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__replicate_0) ).

thf(1924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(160,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(1068,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)],[160]) ).

thf(596,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(2062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(326,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(1443,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)],[326]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).

thf(1618,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

thf(994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(309,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(1401,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)],[309]) ).

thf(19,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).

thf(741,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(453,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

thf(1728,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(80,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).

thf(873,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(389,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_List_Olist_Olist__size @ B @ C @ D ) @ tc_nat )
      | ~ ( c_lessequals @ A @ ( hAPP @ B @ E ) @ tc_nat )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__size__estimation_H_0) ).

thf(1591,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_List_Olist_Olist__size @ B @ C @ D ) @ tc_nat )
      | ~ ( c_lessequals @ A @ ( hAPP @ B @ E ) @ tc_nat )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(82,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).

thf(878,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(438,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(1692,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)],[438]) ).

thf(268,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(1305,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_1) ).

thf(1041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(207,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1173,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(719,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(2363,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(220,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(1200,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(8,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

thf(730,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
        = ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).

thf(1882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
        = ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(317,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(1422,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)],[317]) ).

thf(380,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(1569,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)],[380]) ).

thf(370,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(1544,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)],[370]) ).

thf(576,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__in__set_0) ).

thf(2014,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(652,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(2195,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)],[652]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).

thf(1137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(585,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(2035,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(646,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(2184,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(515,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(1872,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)],[515]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).

thf(1233,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(535,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

thf(1919,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(414,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(1640,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(1063,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(332,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(1458,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)],[332]) ).

thf(165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ A @ ( c_List_Olist__update @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ E @ C ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_1) ).

thf(1078,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ A @ ( c_List_Olist__update @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ E @ C ) @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(319,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).

thf(1426,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(639,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

thf(2168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(249,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(1260,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)],[249]) ).

thf(469,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(1761,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)],[469]) ).

thf(25,axiom,
    class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

thf(747,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).

thf(1507,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(231,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(1222,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)],[231]) ).

thf(103,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(930,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)],[103]) ).

thf(718,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(2360,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)],[718]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Otake @ B @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C ) @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__take__nth__drop_0) ).

thf(1746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Otake @ B @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C ) @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(132,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(1001,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)],[132]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(578,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__takeWhile__le_0) ).

thf(2020,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(603,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(2082,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)],[603]) ).

thf(340,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(1475,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)],[340]) ).

thf(486,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(1803,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)],[486]) ).

thf(120,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(973,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)],[120]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__nth__mono_0) ).

thf(1046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(574,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(2010,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)],[574]) ).

thf(543,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(1935,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)],[543]) ).

thf(641,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_Olist__size @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I1_J_0) ).

thf(2173,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_Olist__size @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(294,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(1366,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)],[294]) ).

thf(598,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(2067,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(556,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).

thf(1967,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(626,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(2136,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)],[626]) ).

thf(251,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(1265,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)],[251]) ).

thf(443,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(1703,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)],[443]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).

thf(1623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(1482,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(705,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ C )
      = ( c_List_Olist_OCons @ D @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).

thf(2328,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ C )
      = ( c_List_Olist_OCons @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(481,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_List_Olist_Olist__size @ B @ C @ D ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ B @ E ) @ tc_nat )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__size__estimation_0) ).

thf(1792,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_List_Olist_Olist__size @ B @ C @ D ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ B @ E ) @ tc_nat )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(587,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

thf(2039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(29,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(751,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)],[29]) ).

thf(49,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(802,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)],[49]) ).

thf(495,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(1826,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)],[495]) ).

thf(257,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(1279,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)],[257]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(622,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).

thf(2126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(334,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(1462,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
        = E )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).

thf(1055,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
        = E )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

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

thf(724,plain,
    class_Int_Onumber @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(423,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1660,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(265,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).

thf(1298,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(509,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(1860,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(660,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(2217,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)],[660]) ).

thf(276,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(1323,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)],[276]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__set__sublistI_0) ).

thf(838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(647,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(2185,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)],[647]) ).

thf(331,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(1455,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)],[331]) ).

thf(111,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(949,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)],[111]) ).

thf(716,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(2356,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)],[716]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(1800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(169,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
        = D )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).

thf(1087,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
        = D )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Onth @ B @ A @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__drop__conv__nth_0) ).

thf(1247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Onth @ B @ A @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(79,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(870,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)],[79]) ).

thf(398,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(1609,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(119,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(969,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Otake @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__takeD_0) ).

thf(881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Otake @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(635,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(2158,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)],[635]) ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).

thf(1641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(473,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(1773,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)],[473]) ).

thf(694,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(2301,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)],[694]) ).

thf(554,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(1963,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(517,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(1875,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)],[517]) ).

thf(537,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(1922,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)],[537]) ).

thf(55,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(817,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).

thf(1892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(300,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(1379,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)],[300]) ).

thf(573,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(2007,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)],[573]) ).

thf(662,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(2222,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)],[662]) ).

thf(547,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(1946,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)],[547]) ).

thf(606,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(2090,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)],[606]) ).

thf(298,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ B @ A )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_0) ).

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ B @ A )
        = ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(64,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(834,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)],[64]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Otake @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Otake @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(676,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(2254,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)],[676]) ).

thf(430,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(1677,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(577,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(2017,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)],[577]) ).

thf(669,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(2237,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)],[669]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).

thf(1415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(267,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(1302,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)],[267]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
      = ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).

thf(1109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
      = ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(410,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1632,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(508,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(1858,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)],[508]) ).

thf(620,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(2122,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)],[620]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
      | ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B )
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).

thf(1581,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
      | ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B )
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(708,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(2335,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)],[708]) ).

thf(118,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(966,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)],[118]) ).

thf(212,axiom,
    c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1183,plain,
    c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(600,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
        = ( c_List_Oappend @ ( c_List_Otake @ B @ A @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ D ) @ D ) @ D ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).

thf(2073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
        = ( c_List_Oappend @ ( c_List_Otake @ B @ A @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ D ) @ D ) @ D ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(153,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(1051,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)],[153]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_1) ).

thf(821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ ( tc_List_Olist @ E ) )
        = ( c_Suc @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__insert_0) ).

thf(981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ ( tc_List_Olist @ E ) )
        = ( c_Suc @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(502,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(1843,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)],[502]) ).

thf(721,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(2367,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)],[721]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(649,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(2190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

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

thf(734,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(77,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(866,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)],[77]) ).

thf(184,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1119,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(306,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(1394,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)],[306]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(1600,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(483,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(162,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(1072,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)],[162]) ).

thf(571,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).

thf(2002,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(671,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(2242,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(126,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).

thf(988,plain,
    class_OrderedGroup_Osemigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(688,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
        = ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

thf(2286,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
        = ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(612,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(2103,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)],[612]) ).

thf(311,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(1405,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)],[311]) ).

thf(546,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(1943,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)],[546]) ).

thf(221,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(1201,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)],[221]) ).

thf(177,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(1104,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)],[177]) ).

thf(440,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(1697,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)],[440]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(1242,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(71,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(849,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(633,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(2154,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)],[633]) ).

thf(360,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(1521,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)],[360]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I1_J_0) ).

thf(1863,plain,
    ! [A: $i] :
      ( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(575,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_3) ).

thf(2011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ D @ C ) ) )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ~ ( c_in @ C @ ( c_List_Oset @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__pos__if__in__set_0) ).

thf(1206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ~ ( c_in @ C @ ( c_List_Oset @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(108,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(942,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)],[108]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(1438,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
      | ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
      | ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
      = ( c_List_Ohd @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).

thf(1306,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
      = ( c_List_Ohd @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(720,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olength__unique @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).

thf(2364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olength__unique @ B @ C ) )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(618,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(2118,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(282,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1338,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(457,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1736,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(513,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(1868,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)],[513]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(395,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(1604,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)],[395]) ).

thf(338,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(1470,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)],[338]) ).

thf(445,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(1708,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)],[445]) ).

thf(271,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1311,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(666,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(2232,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
      | ~ ( 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 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(2000,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
      | ~ ( 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 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(412,axiom,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(1636,plain,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(48,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(798,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)],[48]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(255,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(1274,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)],[255]) ).

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

thf(746,plain,
    class_Orderings_Opreorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Orev @ B @ A ) @ A )
        = ( c_List_Olistsum @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__rev_0) ).

thf(1021,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Orev @ B @ A ) @ A )
        = ( c_List_Olistsum @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(112,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(952,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)],[112]) ).

thf(359,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(1519,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)],[359]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Suc @ B ) )
      | ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(1255,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Suc @ B ) )
      | ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(75,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(862,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(208,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(1174,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)],[208]) ).

thf(464,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(1751,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)],[464]) ).

thf(426,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(1666,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)],[426]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).

thf(1487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

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

thf(729,plain,
    class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(303,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(1387,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)],[303]) ).

thf(527,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(1900,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)],[527]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

thf(1723,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ 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(1217,plain,
    ! [A: $i] :
      ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ 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)],[228]) ).

thf(630,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(2147,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)],[630]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).

thf(1824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(631,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(2150,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).

thf(916,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(394,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(1602,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)],[394]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).

thf(1920,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(1951,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ A @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(492,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(1819,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)],[492]) ).

thf(62,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(830,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)],[62]) ).

thf(644,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(2179,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)],[644]) ).

thf(712,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(2345,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)],[712]) ).

thf(218,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(1195,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)],[218]) ).

thf(305,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(1392,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)],[305]) ).

thf(262,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(1291,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)],[262]) ).

thf(136,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(1012,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)],[136]) ).

thf(544,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_2) ).

thf(1938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ D @ E @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__insort__key_1) ).

thf(847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ D @ E @ A ) @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ D @ E @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(522,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1888,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(264,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(1296,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)],[264]) ).

thf(499,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(1836,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)],[499]) ).

thf(479,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(1787,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)],[479]) ).

thf(699,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(2313,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)],[699]) ).

thf(189,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(1128,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)],[189]) ).

thf(531,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
      = ( hAPP @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).

thf(1910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
      = ( hAPP @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(68,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(842,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(20,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(742,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__append_0) ).

thf(1541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(278,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(1328,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)],[278]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

thf(1498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__drop_0) ).

thf(1006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(518,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).

thf(1878,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(466,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(1755,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)],[466]) ).

thf(183,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).

thf(1118,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(681,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(2268,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(989,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(292,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(1360,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)],[292]) ).

thf(672,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(2245,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(195,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(1143,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)],[195]) ).

thf(617,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(2115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(482,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(1794,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)],[482]) ).

thf(550,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(1953,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
      | ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
        = ( c_List_Oappend @ C @ D @ B ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
      | ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
        = ( c_List_Oappend @ C @ D @ B ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(233,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(1227,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)],[233]) ).

thf(507,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(1856,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)],[507]) ).

thf(3,axiom,
    class_Orderings_Olinorder @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(725,plain,
    class_Orderings_Olinorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(173,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(1096,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)],[173]) ).

thf(428,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(1672,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)],[428]) ).

thf(379,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(1567,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)],[379]) ).

thf(202,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(1160,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)],[202]) ).

thf(580,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).

thf(2023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(555,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ C @ B )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__singleton_0) ).

thf(1964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ C @ B )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) )
      | ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(703,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(2323,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)],[703]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ D @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__sublistD_0) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ D @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(459,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(1739,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)],[459]) ).

thf(91,axiom,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(901,plain,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(318,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(1424,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)],[318]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(1584,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(489,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(1810,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OAbs @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oreplicate @ B @ C @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oreplicate @ B @ C @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(348,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(1493,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)],[348]) ).

thf(433,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(1683,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)],[433]) ).

thf(593,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(2053,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)],[593]) ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).

thf(2240,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(614,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).

thf(2108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(327,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(1446,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)],[327]) ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Odrop @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__dropD_0) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Odrop @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(604,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(2085,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)],[604]) ).

thf(523,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(1889,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)],[523]) ).

thf(416,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(1644,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)],[416]) ).

thf(400,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(1612,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(148,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ E @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_2) ).

thf(1039,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_in @ B @ ( c_List_Oset @ E @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ E @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(200,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(1155,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).

thf(1744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
      = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(474,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

thf(1776,plain,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(559,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(1974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(373,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 @ ( c_COMBC @ c_Lambda_Olift @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ 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(1552,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 @ ( c_COMBC @ c_Lambda_Olift @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(541,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1932,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(157,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1060,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(124,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(984,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)],[124]) ).

thf(564,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).

thf(1984,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(516,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(1874,plain,
    ! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(320,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(1429,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)],[320]) ).

thf(243,axiom,
    class_Power_Opower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(1246,plain,
    class_Power_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(448,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).

thf(1715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Suc @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Suc @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

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

thf(738,plain,
    class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(695,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(2304,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(364,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(1530,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)],[364]) ).

thf(368,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).

thf(1539,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(1831,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(235,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(1231,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)],[235]) ).

thf(561,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1979,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(41,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(779,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)],[41]) ).

thf(407,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(1627,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)],[407]) ).

thf(362,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(1525,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)],[362]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

thf(1333,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(322,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(1434,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)],[322]) ).

thf(655,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(2203,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)],[655]) ).

thf(476,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(1779,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)],[476]) ).

thf(589,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(2043,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)],[589]) ).

thf(99,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(921,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)],[99]) ).

thf(601,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(2076,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)],[601]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).

thf(1466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ C @ B )
        = ( c_List_Olist_ONil @ B ) )
      | ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__singleton_1) ).

thf(1663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ C @ B )
        = ( c_List_Olist_ONil @ B ) )
      | ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(357,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(1515,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)],[357]) ).

thf(402,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(1616,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).

thf(1732,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(101,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(926,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(567,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(1991,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)],[567]) ).

thf(274,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(1318,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)],[274]) ).

thf(35,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(765,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)],[35]) ).

thf(503,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(1846,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)],[503]) ).

thf(260,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(1286,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)],[260]) ).

thf(146,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

thf(1035,plain,
    class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat )
      | ( ( c_List_Onth @ A @ B @ D )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_0) ).

thf(1026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat )
      | ( ( c_List_Onth @ A @ B @ D )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(525,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Onth @ B @ A @ C )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).

thf(1895,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Onth @ B @ A @ C )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__drop_0) ).

thf(773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(709,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_ONil @ D ) @ D @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I1_J_0) ).

thf(2338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_ONil @ D ) @ D @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(529,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(1906,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)],[529]) ).

thf(470,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(1764,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)],[470]) ).

thf(584,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(2033,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)],[584]) ).

thf(539,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__in__set_0) ).

thf(1927,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

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

thf(745,plain,
    class_Orderings_Oorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(678,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
        = A )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).

thf(2260,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
        = A )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(668,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(2235,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(629,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(2144,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)],[629]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ D )
        = C )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__eq_0) ).

thf(906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ D )
        = C )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).

thf(1135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(418,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(1648,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(28,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

thf(750,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(355,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Omap @ A @ B @ C @ D ) @ E @ D )
        = ( hAPP @ A @ ( c_List_Onth @ B @ E @ C ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ E @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__map_0) ).

thf(1510,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Omap @ A @ B @ C @ D ) @ E @ D )
        = ( hAPP @ A @ ( c_List_Onth @ B @ E @ C ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ E @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

thf(1146,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(690,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(2292,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)],[690]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).

thf(1959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(176,axiom,
    class_Nat_Osemiring__char__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).

thf(1103,plain,
    class_Nat_Osemiring__char__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(229,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(1219,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)],[229]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__equals__nth__mono_0) ).

thf(824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(582,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(2028,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)],[582]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(1595,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(409,axiom,
    class_Nat_Osemiring__char__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(1631,plain,
    class_Nat_Osemiring__char__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(11,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).

thf(733,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(57,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(819,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)],[57]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(904,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(591,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(2048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(10,axiom,
    class_Ring__and__Field_Oidom @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

thf(732,plain,
    class_Ring__and__Field_Oidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(648,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(2188,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)],[648]) ).

thf(404,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(1620,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)],[404]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__nil_0) ).

thf(1652,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(21,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

thf(743,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(60,axiom,
    class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).

thf(826,plain,
    class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(366,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(1535,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)],[366]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(1701,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(187,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(1124,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)],[187]) ).

thf(625,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(2134,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(478,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(1784,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)],[478]) ).

thf(304,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(1389,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)],[304]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__take_0) ).

thf(958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(310,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(1403,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)],[310]) ).

thf(194,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(1139,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)],[194]) ).

thf(427,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(1669,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)],[427]) ).

thf(691,axiom,
    ! [A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).

thf(2293,plain,
    ! [A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(272,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(1312,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)],[272]) ).

thf(512,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(1865,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)],[512]) ).

thf(171,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(1092,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)],[171]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).

thf(1090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(50,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(804,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)],[50]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(1464,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C )
        = ( c_List_Odrop @ B @ A @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__drop_H_0) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C )
        = ( c_List_Odrop @ B @ A @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(254,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(1271,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)],[254]) ).

thf(697,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(2308,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)],[697]) ).

thf(297,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).

thf(1371,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(156,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(1058,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)],[156]) ).

thf(178,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ C @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Oinsort__key @ B @ E @ C @ D @ A ) @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__insort__key_0) ).

thf(1107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ C @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Oinsort__key @ B @ E @ C @ D @ A ) @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(239,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(1239,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(569,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(1997,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)],[569]) ).

thf(717,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(2358,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)],[717]) ).

thf(290,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(1356,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)],[290]) ).

thf(602,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(2079,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)],[602]) ).

thf(90,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(900,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
      = ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ C @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
      = ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ C @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(665,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Otake @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__take_0) ).

thf(2229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Otake @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(659,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__replicate_0) ).

thf(2214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(43,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(784,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(382,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(1574,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)],[382]) ).

thf(186,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(1122,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)],[186]) ).

thf(437,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(1690,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)],[437]) ).

thf(557,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(1969,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)],[557]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).

thf(1853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(312,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(1408,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)],[312]) ).

thf(152,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(1048,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(14,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

thf(736,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_0) ).

thf(1349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(609,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(2097,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(130,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(996,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)],[130]) ).

thf(542,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(1933,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)],[542]) ).

thf(677,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(2257,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)],[677]) ).

thf(388,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(1589,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)],[388]) ).

thf(472,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(1771,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)],[472]) ).

thf(15,axiom,
    class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).

thf(737,plain,
    class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(381,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_0) ).

thf(1571,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ A @ B )
        = ( c_List_Onth @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__conv__nth_0) ).

thf(1376,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ A @ B )
        = ( c_List_Onth @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(86,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(890,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)],[86]) ).

thf(645,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).

thf(2182,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(581,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(2025,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)],[581]) ).

thf(32,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(758,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)],[32]) ).

thf(623,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(2129,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)],[623]) ).

thf(615,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(2111,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)],[615]) ).

thf(568,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(1993,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)],[568]) ).

thf(454,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

thf(1731,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(675,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(2252,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)],[675]) ).

thf(685,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 @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ C @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ D @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ 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(2278,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 @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ C @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ D @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(74,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(858,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)],[74]) ).

thf(375,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(1557,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)],[375]) ).

thf(530,axiom,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I4_J_0) ).

thf(1909,plain,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(4,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).

thf(726,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(143,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(1029,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)],[143]) ).

thf(88,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ 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__increasing__iff_1) ).

thf(895,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ 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)],[88]) ).

thf(198,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(1149,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)],[198]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
      = ( c_List_Olist__update @ A @ B @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

thf(964,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
      = ( c_List_Olist__update @ A @ B @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).

thf(1460,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(689,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(2289,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(209,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(1177,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)],[209]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

thf(1381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(714,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(2350,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)],[714]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).

thf(1699,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(658,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(2212,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)],[658]) ).

thf(597,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(2064,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OVar @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Oset @ A @ C ) @ C )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__mem_0) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Oset @ A @ C ) @ C )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(341,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(1477,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)],[341]) ).

thf(611,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(2101,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)],[611]) ).

thf(349,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).

thf(1496,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(72,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(851,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)],[72]) ).

thf(634,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ 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_diff__Suc__less_0) ).

thf(2156,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ 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)],[634]) ).

thf(439,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(1694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

thf(1805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(377,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(1562,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)],[377]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(206,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(1171,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)],[206]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(1198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).

thf(1841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(1396,plain,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(226,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(1213,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)],[226]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
       != D )
      | ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
       != A )
      | ( C
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
      | ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
        = ( c_List_Oappend @ A @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).

thf(768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
       != D )
      | ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
       != A )
      | ( C
       != ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
      | ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
        = ( c_List_Oappend @ A @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
       != A )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( ( c_List_Oappend @ C @ D @ B )
        = ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).

thf(827,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
       != A )
      | ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( ( c_List_Oappend @ C @ D @ B )
        = ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).

thf(2051,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(150,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(1044,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).

thf(1066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(78,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(868,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)],[78]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(2139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(84,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(883,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)],[84]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).

thf(1726,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(245,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
      = ( hAPP @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).

thf(1250,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
      = ( hAPP @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).

thf(1076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(224,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(1208,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)],[224]) ).

thf(109,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(944,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)],[109]) ).

thf(701,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(2318,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)],[701]) ).

thf(621,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).

thf(2124,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(107,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(939,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)],[107]) ).

thf(339,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).

thf(1472,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).

thf(754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(65,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(836,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)],[65]) ).

thf(1,negated_conjecture,
    ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(722,plain,
    ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(548,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(1948,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)],[548]) ).

thf(468,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(1758,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)],[468]) ).

thf(204,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(1166,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)],[204]) ).

thf(53,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
        = ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

thf(812,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
        = ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(354,axiom,
    class_Int_Onumber @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(1509,plain,
    class_Int_Onumber @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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__increasing__iff_0) ).

thf(1081,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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)],[166]) ).

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

thf(749,plain,
    class_Int_Onumber__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(707,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(2333,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(139,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(1018,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)],[139]) ).

thf(371,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(1547,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)],[371]) ).

thf(133,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).

thf(1003,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
        = ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(73,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(855,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)],[73]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(553,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
      = ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).

thf(1961,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
      = ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(161,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(1070,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)],[161]) ).

thf(399,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(1611,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(17,axiom,
    class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

thf(739,plain,
    class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(174,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(1098,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)],[174]) ).

thf(484,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(1798,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)],[484]) ).

thf(693,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(2298,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)],[693]) ).

thf(650,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_Olist__size @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osize_I1_J_0) ).

thf(2192,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_Olist__size @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(887,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

thf(1941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(246,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(1252,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)],[246]) ).

thf(295,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(1368,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)],[295]) ).

thf(642,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(2175,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)],[642]) ).

thf(465,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(1753,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)],[465]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(344,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(1484,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)],[344]) ).

thf(636,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).

thf(2160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(607,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(2092,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)],[607]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev_0) ).

thf(1085,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(431,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(1679,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)],[431]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_0) ).

thf(1130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(446,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).

thf(1711,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(154,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(1053,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)],[154]) ).

thf(480,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(1790,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)],[480]) ).

thf(565,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(1987,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)],[565]) ).

thf(663,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

thf(2224,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(1432,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(638,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( B = E )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).

thf(2165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( B = E )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( 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_Oappend @ C @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).

thf(1813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( ( 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_Oappend @ C @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(266,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(1300,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)],[266]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).

thf(1637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(250,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(1262,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)],[250]) ).

thf(237,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(1235,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)],[237]) ).

thf(684,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(2276,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(661,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(2219,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)],[661]) ).

thf(562,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(1980,plain,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(22,axiom,
    class_Power_Opower @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

thf(744,plain,
    class_Power_Opower @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(526,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).

thf(1898,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
      = ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(616,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(2113,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)],[616]) ).

thf(76,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(864,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)],[76]) ).

thf(463,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(1749,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)],[463]) ).

thf(135,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(1008,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(583,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_OtakeWhile @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__nth_0) ).

thf(2030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_OtakeWhile @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ B @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(81,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(876,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)],[81]) ).

thf(240,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(1240,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)],[240]) ).

thf(594,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(2056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(1358,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(673,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Olast @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).

thf(2247,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Olast @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(230,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(1221,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)],[230]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(558,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(1972,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)],[558]) ).

thf(702,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(2320,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)],[702]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
        = ( c_List_Olist_ONil @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__all_0) ).

thf(1504,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
        = ( c_List_Olist_ONil @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(5,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).

thf(727,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(172,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(1094,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)],[172]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( A
        = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).

thf(978,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( A
        = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(1839,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(605,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(2088,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)],[605]) ).

thf(590,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(2045,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)],[590]) ).

thf(651,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(2194,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(358,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).

thf(1517,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(704,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
        = B )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__all_0) ).

thf(2325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
        = B )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

thf(1126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).

thf(1157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(498,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(1834,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)],[498]) ).

thf(698,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).

thf(2310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ B @ C )
      = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ B @ C )
      = ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(713,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).

thf(2347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_Suc @ ( c_List_Olength__unique @ B @ C ) ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_1) ).

thf(1654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_Suc @ ( c_List_Olength__unique @ B @ C ) ) )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(477,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(1781,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)],[477]) ).

thf(657,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_OtakeWhile @ A @ B @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).

thf(2209,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
        = ( c_List_OtakeWhile @ A @ B @ D ) )
      | ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(328,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(1448,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)],[328]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(696,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(2305,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)],[696]) ).

thf(711,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
        = B )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

thf(2342,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
        = B )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(69,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

thf(844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(664,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).

thf(2226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(330,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(1453,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)],[330]) ).

thf(456,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(1734,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)],[456]) ).

thf(488,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).

thf(1807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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__le__imp__le__exp_0) ).

thf(771,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ ( 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)],[37]) ).

thf(256,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(1276,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)],[256]) ).

thf(417,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(1646,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)],[417]) ).

thf(277,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

thf(1326,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

thf(1721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
      = ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(683,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(2273,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)],[683]) ).

thf(687,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(2283,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)],[687]) ).

thf(429,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(1674,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

thf(1903,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(361,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(1523,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)],[361]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(781,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(632,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(2152,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)],[632]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(610,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(2098,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)],[610]) ).

thf(26,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

thf(748,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(175,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(1101,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)],[175]) ).

thf(408,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(1629,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)],[408]) ).

thf(572,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ ( c_List_Obutlast @ B @ C ) @ C )
        = ( c_List_Otake @ A @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__butlast_0) ).

thf(2004,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ ( c_List_Obutlast @ B @ C ) @ C )
        = ( c_List_Otake @ A @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(242,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

thf(1244,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(493,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(9,axiom,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

thf(731,plain,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(44,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(786,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(510,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(1861,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)],[510]) ).

thf(347,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(1491,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)],[347]) ).

thf(436,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(1689,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist__update @ B @ C @ A @ D ) @ D ) @ D )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__update__memI_0) ).

thf(914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist__update @ B @ C @ A @ D ) @ D ) @ D )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(588,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).

thf(2041,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(475,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(1777,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)],[475]) ).

thf(263,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

thf(1294,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 @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).

thf(1661,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(619,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(2120,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)],[619]) ).

thf(63,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(832,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)],[63]) ).

thf(586,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(2036,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)],[586]) ).

thf(700,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
        = ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__conv__app__nth_0) ).

thf(2315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
        = ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(401,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(1614,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)],[401]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).

thf(1440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
       != ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( A
        = ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
      | ( D
        = ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(706,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Ohd @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).

thf(2330,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
        = ( c_List_Ohd @ A @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(270,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(1308,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)],[270]) ).

thf(653,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(2198,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)],[653]) ).

thf(444,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(1706,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)],[444]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).

thf(1193,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(397,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(1607,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)],[397]) ).

thf(34,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(763,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)],[34]) ).

thf(191,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(1133,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)],[191]) ).

thf(286,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(1348,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)],[286]) ).

thf(384,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(1578,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)],[384]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(1625,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(56,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(818,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).

thf(1593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
        = ( c_List_Onth @ A @ E @ D ) )
      | ( B = E )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_1) ).

thf(790,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
        = ( c_List_Onth @ A @ E @ D ) )
      | ( B = E )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(467,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(1757,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(342,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).

thf(1480,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(13,axiom,
    class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

thf(735,plain,
    class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).

thf(1116,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(628,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(2142,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)],[628]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ C ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__length__takeWhile_0) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ C ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(667,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(2233,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)],[667]) ).

thf(363,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(1527,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)],[363]) ).

thf(197,axiom,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).

thf(1148,plain,
    hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(323,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(1436,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)],[323]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(1363,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(491,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(1816,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)],[491]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(1657,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__nth_2) ).

thf(807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ A @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_0) ).

thf(897,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
        = ( c_List_Onth @ A @ D @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_lessequals @ D @ C @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__rev__nth__mono_0) ).

thf(960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_List_Onth @ B @ C @ A ) @ ( c_List_Onth @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) @ tc_nat )
      | ~ ( c_lessequals @ D @ C @ tc_nat )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(955,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(47,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(796,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)],[47]) ).

thf(654,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).

thf(2201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(98,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(918,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)],[98]) ).

thf(566,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).

thf(1989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(281,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(1335,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)],[281]) ).

thf(599,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(2070,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)],[599]) ).

thf(145,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(1033,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)],[145]) ).

thf(261,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(1288,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)],[261]) ).

thf(579,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
      = ( c_List_Onth @ B @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).

thf(2021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
      = ( c_List_Onth @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(285,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(1346,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)],[285]) ).

thf(460,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(1742,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)],[460]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ A @ B @ ( c_List_Onth @ A @ B @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).

thf(928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ A @ B @ ( c_List_Onth @ A @ B @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

thf(1352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(496,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).

thf(1829,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ D )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).

thf(1152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ D )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__drop_0) ).

thf(1532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(680,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(2265,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(128,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(992,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)],[128]) ).

thf(447,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(1713,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)],[447]) ).

thf(519,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(1880,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)],[519]) ).

thf(521,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(1885,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)],[521]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).

thf(1120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(540,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(1930,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)],[540]) ).

thf(715,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(2353,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)],[715]) ).

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

thf(728,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(18,axiom,
    class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

thf(740,plain,
    class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(302,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ D @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ E @ F @ A ) @ F ) )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_1) ).

thf(1384,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_List_Olinorder__class_Oinsort__key @ B @ C @ ( c_List_Olist_OCons @ D @ E @ F ) @ F @ A )
        = ( c_List_Olist_OCons @ D @ ( c_List_Olinorder__class_Oinsort__key @ B @ C @ E @ F @ A ) @ F ) )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(367,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(1537,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)],[367]) ).

thf(560,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( A
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

thf(1976,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist__update @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( A
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).

thf(1550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_List_Oset @ D @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).

thf(1399,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(682,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2270,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_4) ).

thf(1320,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
        = ( c_List_Otake @ D @ B @ C ) )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Onth @ B @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ A @ D @ B @ C ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(534,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).

thf(1917,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(640,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(2170,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)],[640]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(1204,plain,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(613,axiom,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(2106,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(337,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(1468,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)],[337]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).

thf(1912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(643,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).

thf(2177,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1331,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(396,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(1606,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(100,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(923,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)],[100]) ).

thf(656,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(2206,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)],[656]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

thf(1737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(432,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(1681,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)],[432]) ).

thf(213,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(1184,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)],[213]) ).

thf(504,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(1848,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)],[504]) ).

thf(595,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(2059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).

thf(1490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).

thf(775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ C @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).

thf(1014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ B @ C @ D ) @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ C @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(315,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(1417,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)],[315]) ).

thf(514,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(1870,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)],[514]) ).

thf(2372,plain,
    $false,
    inference(cvc4,[status(thm)],[2163,1036,1718,1024,1369,2131,1633,1767,2263,1559,1237,893,1179,777,1956,1586,1501,809,2094,1411,1168,2295,2341,909,1031,1315,1850,1083,962,1982,2280,1554,1686,2250,1211,1924,1068,2062,1443,1618,994,1401,741,1728,873,1591,1269,878,1692,1305,1041,1173,2363,1200,730,1882,1422,1569,1544,2014,2195,1137,2035,2184,1872,1233,1919,1640,1063,1354,1458,1078,1426,2168,1260,1761,747,1507,1222,930,2360,1746,1001,1914,1576,2020,1650,2082,1475,1803,973,1046,2010,1935,2173,1366,2067,1967,2136,1265,1703,1623,1482,2328,1792,2039,751,802,1826,1279,1191,2126,1462,1055,724,1660,1298,1860,2217,1323,838,2185,1455,949,2356,1800,1087,1247,870,1609,969,881,2158,1641,1773,2301,1963,1875,1922,817,1892,1379,2007,2222,1946,2090,1373,834,937,2254,1677,2017,2237,1415,1302,756,1109,1632,1858,2122,1581,2335,966,1183,2073,1051,821,981,1843,2367,1215,2190,734,866,1119,1394,1600,1796,1072,2002,998,2242,988,2286,2103,1405,1943,1201,1104,1697,1242,849,2154,1521,1863,2011,1206,942,1438,793,1306,2364,761,2118,1338,1736,1868,1074,1604,1470,1708,1311,2232,2000,1636,798,1163,1274,746,1343,1021,952,1519,1255,862,1174,1751,1666,1487,815,729,1387,1900,1723,1217,2147,1824,2150,916,1602,1920,1951,1687,1819,830,2179,2345,1195,1392,1291,1012,1938,847,1888,1296,1836,1787,2313,1128,1910,842,742,1541,1328,1498,1006,1878,1755,1118,2268,989,1360,2245,1143,2115,1794,1953,1111,1227,1856,725,1096,1672,1567,1160,2023,1964,2323,933,1739,901,1424,1584,1810,1419,1493,1683,2053,2240,2108,1446,1016,2085,1889,1644,1612,1039,1155,1744,1114,1776,1974,1552,1932,1060,984,1984,1874,1429,1246,1715,1451,738,2304,1530,1539,1831,1231,1979,779,1627,1525,1333,1434,2203,1779,2043,921,2076,1466,1187,1663,1515,1616,1732,926,1991,1318,765,1846,1286,1035,1026,1895,773,2338,1906,1764,2033,1927,745,2260,2235,2144,906,1135,1648,750,1510,1146,2292,1959,1103,1219,824,2028,1595,1631,733,819,904,2048,732,2188,1620,1652,743,826,1535,1701,1124,2134,1784,1389,958,1403,1139,1669,2293,1312,1865,1092,1090,804,1258,1464,1224,1271,2308,1371,1058,1107,1239,1997,2358,1356,2079,900,1282,2229,2214,784,1574,1122,1690,1969,1853,1408,1048,736,1349,2097,996,1933,2257,1589,1771,737,1571,1376,890,2182,2025,758,2129,2111,1993,1731,2252,2278,858,1557,1909,726,1029,895,1149,964,1460,2289,1177,1381,2350,1699,2212,2064,986,1477,2101,1496,851,2156,1694,1805,1562,912,1171,1198,1841,1396,1213,768,827,2051,1044,1066,868,2139,883,1726,1250,1076,1208,944,2318,2124,939,1472,754,1181,836,722,1948,1758,1166,812,1509,1081,749,2333,1018,1547,1003,855,1598,1961,1070,1611,739,1098,1798,2298,2192,887,1941,1252,1368,2175,1753,1267,1484,2160,2092,840,1085,1679,1130,1711,1053,1790,1987,2224,1432,2165,1813,1300,1637,1262,1235,2276,2219,1980,744,1898,2113,864,1749,1008,2030,876,1240,2056,1358,2247,1221,1284,1972,2320,1504,727,1094,978,1839,2088,2045,2194,1517,2325,1126,1157,1834,2310,976,2347,1654,1781,2209,1448,1189,2305,2342,844,2226,1453,1734,1807,771,1276,1646,1326,1721,2273,2283,1674,1903,1523,781,2152,1341,2098,748,946,1101,1629,2004,1244,1822,731,786,1861,1491,1689,914,2041,1777,1294,1513,1661,2120,832,2036,2315,1614,1440,2330,1308,2198,1706,1193,1607,763,1133,1348,1578,1625,818,1593,790,1757,1480,735,1116,2142,1229,2233,1527,1148,1436,1363,1816,1657,807,897,960,955,796,2201,918,1989,1335,2070,1033,1288,2021,1346,1742,928,1352,1829,1152,1532,2265,992,1713,1880,1885,1120,1930,2353,728,740,1384,1537,1976,1550,1399,2270,1320,935,1565,1917,2170,1204,2106,1468,1912,2177,1331,1606,923,2206,1737,1681,1184,1848,2059,1490,775,1014,1417,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 16:01:54 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.98/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.67/1.13  % [INFO] 	 Parsing done (233ms). 
% 1.67/1.14  % [INFO] 	 Running in sequential loop mode. 
% 2.32/1.33  % [INFO] 	 eprover registered as external prover. 
% 2.32/1.33  % [INFO] 	 cvc4 registered as external prover. 
% 2.32/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.80/1.47  % [INFO] 	 Found a conjecture and 722 axioms. Running axiom selection ... 
% 3.13/1.60  % [INFO] 	 Axiom selection finished. Selected 720 axioms (removed 2 axioms). 
% 4.13/1.77  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.16/1.79  % [INFO] 	 Type checking passed. 
% 4.16/1.79  % [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 ... 
% 11.74/3.59  % External prover 'cvc4' found a proof!
% 11.74/3.59  % [INFO] 	 Killing All external provers ... 
% 11.74/3.59  % Time passed: 3068ms (effective reasoning time: 2451ms)
% 11.74/3.59  % 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)>
% 11.74/3.59  % Axioms used in derivation (720): cls_not__one__less__zero_0, cls_less__iff__diff__less__0_0, cls_linorder__antisym__conv2_1, cls_subst__lt_0, cls_power__0_0, cls_App__eq__foldl__conv_3, cls_le__0__eq_1, cls_subst__map_0, cls_dB_Osimps_I6_J_0, cls_take__eq__Nil_0, cls_butlast__snoc_0, cls_Suc__pred_0, cls_Nil__is__rev__conv_1, cls_list__size__estimation_0, cls_Nil__is__map__conv_1, cls_last_Osimps_0, cls_dB_Osplit_0, cls_list__update__same__conv_1, cls_add__0__left_0, cls_last__drop_0, cls_xt1_I9_J_0, cls_append__eq__append__conv__if_3, cls_sorted__append_2, cls_add__pos__nonneg_0, cls_nth__list__update__neq_0, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_rev__swap_1, cls_last_Osimps_1, cls_less__diff__iff_1, cls_zero__less__one_0, clsarity_Int__Oint__Int_Onumber, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_eq__imp__le_0, cls_nth__Cons_H_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_nth__Cons__number__of_0, cls_le__diff__iff_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_in__listsp__conv__set_0, cls_of__nat__0_0, cls_list__update__overwrite_0, cls_Nat_Odiff__diff__eq_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_append__self__conv_0, cls_butlast_Osimps_I1_J_0, cls_take__Suc__conv__app__nth_0, cls_in__set__butlast__appendI_1, cls_drop__append_0, cls_take__0_0, cls_nth__take_0, cls_map__replicate_0, cls_set__ConsD_0, cls_dB_Osimps_I8_J_0, cls_insort__key_Osimps_I2_J_1, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_zero__le__one_0, cls_takeWhile__eq__take__P__nth_2, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_splice__Cons__Cons_0, cls_eq__diff__iff_0, cls_append__step1I_0, cls_replicate__empty_0, cls_power__inject__exp_0, cls_nth__list__update__eq_0, cls_less__antisym_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_linorder__neqE_0, cls_listsum_Osimps_I1_J_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_CHAINED_0, cls_power__increasing_0, cls_in__set__conv__decomp_1, cls_of__nat__less__iff_0, cls_Cons__eq__map__conv_3, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_nth__mem_0, cls_take__Cons_H_0, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_add__le__cancel__left_1, cls_nth__list__update_0, cls_Snoc__step1__SnocD_2, cls_not__Cons__self2_0, cls_not__less__eq_1, cls_dB_Osimps_I12_J_0, cls_rev__is__rev__conv_0, cls_mem__def_1, cls_add__le__cancel__right_1, cls_append__eq__append__conv__if_6, clsarity_nat__Orderings_Olinorder, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_list__update__append_1, cls_less__Suc__eq_2, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_hd__conv__nth_0, cls_power__le__imp__le__exp_0, cls_dB_Osplit__asm_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_of__nat__0__less__iff_0, cls_Cons__step1__Cons_5, cls_add__left__cancel_0, cls_power__less__imp__less__exp_0, cls_head__Var__reduction_1, cls_comm__monoid__add_Omult__1__right_0, cls_drop__0_0, cls_list__update__nonempty_1, cls_power__one_0, cls_id__take__nth__drop_0, 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_add__cancel__21_1, cls_same__append__eq_0, cls_beta_0, cls_append__Cons_0, cls_listsum__append_0, cls_gr0I_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_hd__append_0, cls_length__map_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_add__nonneg__pos_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_butlast_Osimps_I2_J_1, cls_le__0__eq_0, cls_takeWhile__append1_0, cls_in__set__takeD_0, cls_Nil__is__map__conv_0, cls_drop__map_0, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_drop__Cons__number__of_0, clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_sorted_Osimps_I3_J_1, cls_diff__diff__cancel_0, cls_order__less__asym_0, cls_sorted__takeWhile_0, cls_of__nat__le__iff_1, cls_nat__less__cases_0, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_in__set__conv__decomp__first_2, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_nth__Cons__Suc_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_add__right__mono_0, cls_append1__eq__conv_1, cls_less__iff__diff__less__0_1, cls_listsum_Osimps_I2_J_0, cls_order__eq__refl_0, clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add, cls_order__le__less_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_set__update__memI_0, cls_in__set__conv__nth_2, cls_length__greater__0__conv_1, cls_of__nat__le__iff_0, cls_linorder__antisym__conv2_0, cls_power__0__left_0, cls_takeWhile__eq__take_0, cls_splice_Osimps_I2_J_0, cls_eq__number__of_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_sorted__take_0, cls_takeWhile_Osimps_I1_J_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_replicate__append__same_0, cls_list__update__beyond_0, cls_Suc__leI_0, cls_rev_Osimps_I2_J_0, cls_nth__via__drop_0, cls_rev__map_0, cls_linorder__neqE__nat_0, cls_hd__append_1, cls_list__update__append1_0, cls_drop__Suc__Cons_0, cls_rev__singleton__conv_0, cls_dB_Osimps_I3_J_0, cls_in__set__conv__decomp__last_2, cls_nth__map_0, cls_foldl__absorb0_0, clsarity_bool__Orderings_Oorder, cls_list__update__same__conv_0, cls_subst__Var_2, cls_xt1_I10_J_0, cls_takeWhile__eq__take__P__nth_3, cls_add__nonneg__eq__0__iff_0, cls_add__less__cancel__right_1, cls_append__self__conv2_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_dB_Osimps_I11_J_0, clsarity_Int__Oint__Int_Oring__char__0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_add__left__mono_0, cls_sorted__equals__nth__mono_0, cls_append__Nil2_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_in__set__butlast__appendI_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semidom, cls_in__set__replicateD_0, cls_add__strict__left__mono_0, cls_power__0__Suc_0, cls_Nitpick_Olist__size__simp_I1_J_0, cls_of__nat__0__le__iff_0, cls_sorted__drop_0, cls_le__iff__diff__le__0_0, cls_sorted_Osimps_I3_J_2, cls_dB_Osimps_I4_J_0, cls_nat__diff__split_0, cls_self__append__conv2_0, cls_insort__key_Osimps_I2_J_0, cls_takeWhile__tail_0, cls_length__0__conv_0, cls_App__eq__foldl__conv_0, cls_hd__drop__conv__nth_0, cls_map__eq__Cons__conv_3, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_not__less__eq__eq_1, cls_self__append__conv2_1, cls_Cons__step1__Cons_1, cls_append__eq__append__conv__if_4, cls_typing__elims_I1_J_0, cls_map__update_0, cls_replicate__Suc_0, cls_append__is__Nil__conv_2, cls_Suc__neq__Zero_0, cls_length__list__update_0, cls_map__is__Nil__conv_0, clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors, cls_Var__IT_0, cls_Cons__step1__Cons_3, cls_append__eq__Cons__conv_5, cls_less__Suc__eq__le_1, cls_append__in__listsp__conv_1, cls_last__in__set_0, cls_power__eq__0__iff_2, cls_append__Nil_0, cls_class__semiring_Oadd__a_0, cls_append__in__listsp__conv_0, cls_last__append_1, cls_append__eq__append__conv2_5, cls_sorted__insort__key_0, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_takeWhile__nth_0, cls_length__unique_Osimps_I1_J_0, cls_take__map_0, cls_of__nat__diff_0, cls_dB_Osimps_I10_J_0, cls_add__right__cancel_0, cls_xt1_I8_J_0, cls_nth__append_0, cls_apps__preserves__betas_0, cls_rev__is__Nil__conv_0, cls_Snoc__step1__SnocD_3, cls_nth__append_1, cls_list__size__estimation_H_0, cls_comm__monoid__add_Omult__commute_0, clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_sorted__nth__mono_0, cls_of__nat__eq__iff_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_take__hd__drop_0, cls_foldl__Cons_0, cls_set__rev_0, cls_sublist__singleton_1, cls_linorder__linear_0, cls_replicate__app__Cons__same_0, cls_power__strict__mono_0, cls_zero__less__two_0, clsarity_Int__Oint__OrderedGroup_Ogroup__add, cls_of__nat__0__less__iff_1, cls_add__strict__mono_0, cls_list__update__append_0, cls_lessI_0, cls_Suc__le__mono_1, cls_replicate__eq__replicate_1, cls_head__Var__reduction_0, cls_less__add__one_0, cls_not__leE_0, cls_le__SucE_0, cls_power__strict__decreasing_0, cls_splice__Nil2_0, cls_zero__less__power_0, cls_order__antisym_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_butlast__append_0, cls_list__update__code_I2_J_0, cls_append__step1I_1, cls_le__number__of__eq__not__less_1, cls_in__set__butlastD_0, cls_not__Cons__self_0, cls_sublist__nil_0, cls_dB_Osimps_I1_J_0, cls_self__append__conv_1, cls_apps__eq__Abs__conv_2, cls_take__append_0, cls_Abs__App__neq__Var__apps_0, cls_map__eq__imp__length__eq_0, cls_lift__map_0, cls_add__cancel__21_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_less__Suc__eq__0__disj_3, clsarity_Int__Oint__Ring__and__Field_Omult__zero, cls_class__semiring_Osemiring__rules_I5_J_0, cls_linorder__antisym__conv1_1, cls_length__greater__0__conv_0, cls_append__same__eq_0, clsarity_bool__Orderings_Opreorder, cls_append__eq__conv__conj_0, cls_last__append_0, cls_zero__neq__one_0, cls_list__update__swap_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_last__snoc_0, cls_mem__def_0, cls_subst__Var_1, cls_append__take__drop__id_0, cls_Cons__step1__Cons_2, cls_splice_Osimps_I1_J_0, cls_diff__self_0, cls_butlast__drop_0, cls_less__imp__diff__less_0, cls_diff__is__0__eq_0, cls_drop__Cons_H_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_diff__less_0, cls_sorted__Cons_0, cls_length__rev_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_linorder__not__le_1, cls_append__assoc_0, cls_nth__drop_H_0, cls_not__Nil__step1_0, cls_append__eq__append__conv__if_1, cls_dB_Osize_I4_J_0, cls_add__less__cancel__right_0, cls_listsum_0, cls_takeWhile__eq__take__P__nth_4, cls_add__diff__cancel_0, cls_butlast__append_1, cls_le__trans_0, cls_drop__Nil_0, cls_neq0__conv_1, cls_apps__eq__Abs__conv_1, clsarity_Int__Oint__Orderings_Olinorder, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_lifts__IT_0, clsarity_nat__Orderings_Opreorder, cls_not__less__iff__gr__or__eq_1, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_Var__apps__neq__Abs__apps_0, cls_Suc__le__eq_0, clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add, cls_foldl__assoc_0, cls_sorted__insort__key_1, cls_length__pos__if__in__set_0, cls_App_I4_J_0, cls_drop__butlast_0, cls_nth__length__takeWhile_0, clsarity_nat__Int_Onumber, clsarity_Int__Oint__Ring__and__Field_Osemiring__0, cls_order__le__neq__trans_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_last__rev_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_add__nonneg__eq__0__iff_1, cls_take__eq__Nil_2, cls_diff__less__Suc_0, cls_Cons__step1__Cons_4, cls_right__minus__eq_1, cls_linorder__neqE__ordered__idom_0, cls_map__append_0, cls_less__le__not__le_1, cls_sublist__singleton_0, cls_Suc__diff__diff_0, cls_dB_Osimps_I2_J_1, clsarity_Int__Oint__Orderings_Opreorder, cls_add__nonneg__nonneg_0, cls_empty__replicate_0, cls_dB_Osplit__asm_2, cls_class__ringb_Oadd__r0__iff_0, cls_nat_Oinject_0, cls_order__antisym__conv_0, cls_rev__replicate_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_order__le__less_1, cls_linorder__neq__iff_1, cls_sorted_Osimps_I1_J_0, cls_diff__less__mono_0, clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors, cls_add__strict__increasing_0, cls_rev__eq__Cons__iff_1, cls_power__strict__increasing__iff_1, cls_hd__replicate_0, cls_power__le__imp__le__base_0, cls_not__less__less__Suc__eq_1, clsarity_Int__Oint__Power_Opower, cls_drop__replicate_0, cls_list__update__id_0, cls_takeWhile_Osimps_I2_J_1, cls_sorted__append_0, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_power__increasing__iff_1, cls_listsum__rev_0, cls_eq__eqI_0, cls_nat_Osimps_I2_J_0, cls_map__eq__conv_0, cls_Zero__neq__Suc_0, cls_less__eq__Suc__le_0, cls_map__is__Nil__conv_1, cls_Suc__lessD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_le__less__Suc__eq_0, clsarity_Int__Oint__Int_Onumber__ring, cls_zero__less__diff_0, cls_le0_0, cls_rev__is__Nil__conv_1, cls_less__eq__Suc__le_1, cls_Suc__length__conv_2, clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add, cls_last__replicate_0, cls_app__last_0, cls_diff__self__eq__0_0, cls_less__Suc__eq__le_0, cls_append__eq__conv__conj_1, cls_xt1_I11_J_0, cls_map_Osimps_I2_J_0, cls_add__neg__neg_0, cls_dB_Osize_I1_J_0, cls_le__eqI_0, cls_App__eq__foldl__conv_2, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_length__unique_Osimps_I2_J_1, cls_take__Suc__Cons_0, cls_abs_0, cls_less__Suc0_0, cls_Snoc__step1__SnocD_0, cls_Abs__eq__apps__conv_2, cls_le__add__right__mono_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_take__butlast_0, cls_takeWhile__eq__take__P__nth_0, cls_typing_OVar_0, cls_diff__Suc__less_0, cls_diff__le__self_0, cls_lift__IT_0, cls_replicate__eq__replicate_2, cls_IT_OVar_0, clsarity_Int__Oint__OrderedGroup_Omonoid__mult, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_diff__0__right_0, cls_xt1_I6_J_0, clsarity_Int__Oint__Nat_Osemiring__char__0, cls_append__is__Nil__conv_1, cls_takeWhile__eq__all__conv_0, cls_nat__less__le_0, cls_dB_Osplit_1, cls_sorted__rev__nth__mono_0, cls_nat_Osimps_I3_J_0, cls_le__Suc__eq_2, cls_comm__monoid__add_Omult__1_0, cls_length__drop_0, cls_nat__less__le_2, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, clsarity_Int__Oint__Ring__and__Field_Oidom, cls_double__add__less__zero__iff__single__less__zero_1, cls_diff__less__mono2_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_less__trans__Suc_0, cls_Nil__is__rev__conv_0, cls_apps__preserves__beta_0, cls_append__is__Nil__conv_0, cls_add__nonneg__eq__0__iff_2, cls_less__diff__iff_0, cls_append__eq__appendI_0, cls_power__Suc__less__one_0, cls_less__eqI_0, cls_App__eq__foldl__conv_5, cls_set__takeWhileD_1, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_append__eq__append__conv__if_0, cls_hd__in__set_0, cls_order__less__irrefl_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_App__eq__foldl__conv_4, cls_length__Suc__conv_2, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_Suc__n__not__le__n_0, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_zero__less__diff_1, cls_one__less__power_0, clsarity_Int__Oint__OrderedGroup_Oab__group__add, clsarity_fun__Orderings_Opreorder, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add, cls_rev__append_0, cls_n__not__Suc__n_0, cls_App_I2_J_0, cls_power__inject__base_0, cls_rev__nth_0, cls_take__Cons__number__of_0, cls_foldl__append_0, cls_Suc__leD_0, cls_hd_Osimps_0, cls_add__mono_0, cls_less__SucI_0, cls_drop__take_0, cls_add__neg__nonpos_0, cls_take__all_0, cls_not__less0_0, cls_nth__append__length_0, cls_set__takeWhileD_0, cls_dB_Osimps_I5_J_0, cls_diffs0__imp__equal_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_list_Osize_I1_J_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_class__ringb_Osubr0__iff_1, cls_sorted_Osimps_I2_J_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_hd__rev_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_in__set__sublistD_0, clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_foldl__Nil_0, cls_length__takeWhile__le_0, cls_sorted__Cons_1, cls_Suc__less__eq_0, cls_le__iff__diff__le__0_1, cls_lift_Osimps_I1_J_0, cls_zero__le__power_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_length__unique_Osimps_I2_J_0, cls_nth__list__update_1, cls_order__less__imp__le_0, cls_dB_Osplit__asm_1, cls_takeWhile_Osimps_I2_J_0, cls_le__eqI_1, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_Suc__diff__le_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_power__increasing__iff_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, clsarity_Int__Oint__Ring__and__Field_Osemiring__1, cls_takeWhile__eq__take__P__nth_1, cls_diff__commute_0, cls_length__insert_0, cls_insort__key_Osimps_I1_J_0, cls_dB_Osplit_2, cls_le__less__Suc__eq_1, cls_add__strict__increasing2_0, cls_subst__lift_0, cls_le__eq__less__or__eq_0, cls_eq__iff__diff__eq__0_0, cls_Abs__eq__apps__conv_1, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_power__strict__increasing__iff_0, cls_drop__all_0, cls_less__Suc0_1, cls_in__set__dropD_0, cls_drop__eq__Nil_0, cls_of__nat__Suc_0, cls_notin__set__sublistI_0, cls_class__ringb_Osubr0__iff_0, cls_list__update__code_I3_J_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_xt1_I7_J_0, cls_linorder__not__less_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_upd__conv__take__nth__drop_0, cls_rev__rev__ident_0, cls_nth__replicate_0, cls_add__le__cancel__left_0, cls_empty__replicate_1, cls_list_Osimps_I2_J_0, cls_Snoc__step1__SnocD_1, clsarity_nat__OrderedGroup_Osemigroup__add, cls_power__decreasing_0, cls_sorted_Osimps_I3_J_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_le__neq__implies__less_0, cls_not__one__le__zero_0, clsarity_Int__Oint__OrderedGroup_Osemigroup__add, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_le__refl_0, cls_power__0__left_1, cls_takeWhile__eq__take__P__nth_5, cls_add__le__cancel__right_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_le__number__of__eq__not__less_0, cls_list__update__nonempty_0, cls_power__mono_0, cls_App__eq__foldl__conv_1, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_not__less__eq__eq_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom
% 11.74/3.59  % No. of inferences in proof: 1443
% 11.74/3.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3068 ms resp. 2451 ms w/o parsing
% 12.42/3.79  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.42/3.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------