TSTP Solution File: SWV972-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV972-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 05:50:08 EDT 2024

% Result   : Unsatisfiable 8.95s 2.97s
% Output   : Refutation 9.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  550
% Syntax   : Number of formulae    :  998 ( 325 unt; 103 typ;   0 def)
%            Number of atoms       : 1755 ( 798 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives : 12138 ( 828   ~; 860   |;   0   &;10450   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  234 ( 234   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  105 ( 103 usr;  21 con; 0-8 aty)
%            Number of variables   : 3018 (   0   ^3018   !;   0   ?;3018   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_thesis_____type,type,
    v_thesis____: $o ).

thf(c_List_Olist__all2_type,type,
    c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).

thf(c_TypeRel_Owiden_type,type,
    c_TypeRel_Owiden: $i > $i > $i ).

thf(v_P_type,type,
    v_P: $i ).

thf(tc_prod_type,type,
    tc_prod: $i > $i > $i ).

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

thf(tc_String_Ochar_type,type,
    tc_String_Ochar: $i ).

thf(tc_Expr_Oexp_type,type,
    tc_Expr_Oexp: $i > $i ).

thf(v_Us_____type,type,
    v_Us____: $i ).

thf(tc_Type_Oty_type,type,
    tc_Type_Oty: $i ).

thf(c_WellTypeRT_OWTrts_type,type,
    c_WellTypeRT_OWTrts: $i > $i > $i > $i > $i > $o ).

thf(v_h_Ha_____type,type,
    v_h_Ha____: $i ).

thf(v_E_____type,type,
    v_E____: $i ).

thf(v_es_Ha_____type,type,
    v_es_Ha____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Type_Oty_OClass_type,type,
    c_Type_Oty_OClass: $i > $i ).

thf(c_Type_Oty_ONT_type,type,
    c_Type_Oty_ONT: $i ).

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

thf(c_TypeRel_OMethod_type,type,
    c_TypeRel_OMethod: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(c_Expr_Oexp_OVal_type,type,
    c_Expr_Oexp_OVal: $i > $i > $i ).

thf(c_Expr_Oexp_OCall_type,type,
    c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).

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

thf(c_Nat_Onat_Onat__case_type,type,
    c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).

thf(c_Pair_type,type,
    c_Pair: $i > $i > $i > $i > $i ).

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

thf(c_fequal_type,type,
    c_fequal: $i > $i ).

thf(c_Objects_Ohext_type,type,
    c_Objects_Ohext: $i > $i > $o ).

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

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

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

thf(c_WellTypeRT_OWTrt_type,type,
    c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).

thf(c_Progress_OWTrt_H_type,type,
    c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).

thf(c_WellType_OWT_type,type,
    c_WellType_OWT: $i > $i > $i > $i > $o ).

thf(c_Conform_Oconf_type,type,
    c_Conform_Oconf: $i > $i > $i > $i ).

thf(v_sko__local__XIH__1_type,type,
    v_sko__local__XIH__1: $i > $i > $i > $i > $i > $i ).

thf(v_ha_____type,type,
    v_ha____: $i ).

thf(v_esa_____type,type,
    v_esa____: $i ).

thf(c_TypeSafe__Mirabelle_Osconf_type,type,
    c_TypeSafe__Mirabelle_Osconf: $i > $i > $i > $o ).

thf(v_la_____type,type,
    v_la____: $i ).

thf(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

thf(tc_Value_Oval_type,type,
    tc_Value_Oval: $i ).

thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__2_type,type,
    c_Conform_Osko__Conform__Xconfs__Cons2__1__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__1_type,type,
    c_Conform_Osko__Conform__Xconfs__Cons2__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlist__all2__append2__1__1_type,type,
    c_List_Osko__List__Xlist__all2__append2__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlist__all2__append2__1__2_type,type,
    c_List_Osko__List__Xlist__all2__append2__1__2: $i > $i > $i > $i > $i > $i > $i ).

thf(v_v_____type,type,
    v_v____: $i ).

thf(v_C_____type,type,
    v_C____: $i ).

thf(c_Progress_OWTrts_H_type,type,
    c_Progress_OWTrts_H: $i > $i > $i > $i > $i > $o ).

thf(c_List_Osko__List__Xlist__all2__refl__1__1_type,type,
    c_List_Osko__List__Xlist__all2__refl__1__1: $i > $i > $i ).

thf(c_WellType_OWTs_type,type,
    c_WellType_OWTs: $i > $i > $i > $i > $o ).

thf(v_sko__local__XCallParams__Xhyps__2__1_type,type,
    v_sko__local__XCallParams__Xhyps__2__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__CHAINED__1_type,type,
    v_sko__CHAINED__1: $i > $i > $i > $i > $i > $i ).

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2_type,type,
    c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2: $i > $i > $i > $i > $i > $i ).

thf(v_M_____type,type,
    v_M____: $i ).

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

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1_type,type,
    c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__local__XCallParams__2__1_type,type,
    v_sko__local__XCallParams__2__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xlist__all2__append1__1__1_type,type,
    c_List_Osko__List__Xlist__all2__append1__1__1: $i > $i > $i > $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xlist__all2__append1__1__2_type,type,
    c_List_Osko__List__Xlist__all2__append1__1__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Conform_Osko__Conform__Xconfs__conv__map__1__1_type,type,
    c_Conform_Osko__Conform__Xconfs__conv__map__1__1: $i > $i > $i > $i > $i > $i ).

thf(186,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(892,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)],[186]) ).

thf(364,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__trans_0) ).

thf(1322,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(243,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(1036,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)],[243]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(809,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(298,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(1168,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)],[298]) ).

thf(427,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).

thf(1454,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(15,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(479,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)],[15]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).

thf(1295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(276,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(1110,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)],[276]) ).

thf(16,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(481,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)],[16]) ).

thf(193,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(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

thf(628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Otake @ A @ B @ C ) @ C )
        = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__take_0) ).

thf(777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Otake @ A @ B @ C ) @ C )
        = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(51,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(555,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)],[51]) ).

thf(315,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ A @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ B @ K @ L @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_1) ).

thf(1211,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ A @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ B @ K @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ B @ tc_nat ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

thf(1158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ B @ tc_nat ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(403,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrts @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).

thf(1406,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrts @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(120,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(730,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(421,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ F ) )
        = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ E ) ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_1) ).

thf(1443,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ F ) )
        = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ E ) ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(226,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(994,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( v_thesis____
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(449,plain,
    ! [A: $i] :
      ( v_thesis____
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(180,axiom,
    ! [A: $i] :
      ( A
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(878,plain,
    ! [A: $i] :
      ( A
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(75,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(614,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)],[75]) ).

thf(174,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(861,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)],[174]) ).

thf(447,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_1) ).

thf(1497,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(262,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(1078,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)],[262]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).

thf(550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1233,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(335,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(1260,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)],[335]) ).

thf(373,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ E ) )
        = ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ F ) ) )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_2) ).

thf(1342,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ E ) )
        = ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ F ) ) )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(254,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

thf(1063,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(44,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(538,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osplit_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(160,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(829,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)],[160]) ).

thf(310,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(1196,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)],[310]) ).

thf(228,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(1001,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)],[228]) ).

thf(113,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(709,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)],[113]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__tl_0) ).

thf(1386,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).

thf(1475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(89,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(651,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)],[89]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(1243,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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)],[328]) ).

thf(283,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(1127,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)],[283]) ).

thf(139,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(782,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XCallParams__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallParams_I2_J_0) ).

thf(1441,plain,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XCallParams__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(183,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(885,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)],[183]) ).

thf(247,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(1046,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(58,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(570,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)],[58]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
      = ( c_List_Obutlast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(140,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).

thf(785,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(1264,plain,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(77,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(619,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)],[77]) ).

thf(128,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(751,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)],[128]) ).

thf(308,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(1191,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)],[308]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

thf(1115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(272,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(1100,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)],[272]) ).

thf(215,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(969,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).

thf(606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(1,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(448,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(445,axiom,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E____ @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf_0) ).

thf(1494,plain,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E____ @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(130,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(756,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)],[130]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ ( c_Type_Oty_OClass @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(1373,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ ( c_Type_Oty_OClass @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XIH__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IH_1) ).

thf(1418,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XIH__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(18,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(485,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(31,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(514,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).

thf(1051,plain,
    ! [A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(443,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ B @ C @ D @ A @ E @ F ) @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ B @ C @ D @ A @ E @ F ) @ F ) )
      | ~ ( c_List_Olist__all2 @ B @ ( c_List_Oappend @ C @ D @ E ) @ A @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_0) ).

thf(1489,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ B @ C @ D @ A @ E @ F ) @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ B @ C @ D @ A @ E @ F ) @ F ) )
      | ~ ( c_List_Olist__all2 @ B @ ( c_List_Oappend @ C @ D @ E ) @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
        = ( c_List_Olist__update @ ( c_List_Obutlast @ A @ D ) @ B @ C @ D ) )
      | ( B
        = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).

thf(1415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
        = ( c_List_Olist__update @ ( c_List_Obutlast @ A @ D ) @ B @ C @ D ) )
      | ( B
        = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

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

thf(492,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__refl_0) ).

thf(1465,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_ONT ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).

thf(634,plain,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(122,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(734,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)],[122]) ).

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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(956,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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__replicate_0) ).

thf(866,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(280,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(1119,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)],[280]) ).

thf(92,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(660,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)],[92]) ).

thf(227,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(998,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)],[227]) ).

thf(374,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ B @ A @ C @ D @ E @ F ) @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ B @ A @ C @ D @ E @ F ) @ E ) )
      | ~ ( c_List_Olist__all2 @ B @ A @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_0) ).

thf(1345,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Oappend @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ B @ A @ C @ D @ E @ F ) @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ B @ A @ C @ D @ E @ F ) @ E ) )
      | ~ ( c_List_Olist__all2 @ B @ A @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(402,axiom,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

thf(1405,plain,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(28,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(507,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)],[28]) ).

thf(37,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(527,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(3,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(452,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(196,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(920,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)],[196]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(678,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(39,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(529,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)],[39]) ).

thf(418,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(1438,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)],[418]) ).

thf(198,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(925,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)],[198]) ).

thf(356,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(1306,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(311,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(1199,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)],[311]) ).

thf(371,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__widen_0) ).

thf(1338,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(435,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ F ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ E ) ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_2) ).

thf(1470,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ F ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ E ) ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(358,axiom,
    c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ v_E____ @ v_esa____ @ v_Us____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wtes_0) ).

thf(1311,plain,
    c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ v_E____ @ v_esa____ @ v_Us____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(257,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(1067,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)],[257]) ).

thf(296,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(1163,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)],[296]) ).

thf(30,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(512,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)],[30]) ).

thf(204,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(942,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)],[204]) ).

thf(292,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(1153,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)],[292]) ).

thf(132,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ A @ F @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ B @ J @ K @ L @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_0) ).

thf(761,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ A @ F @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ B @ J @ K @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(342,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 ) )
      | ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).

thf(1274,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 ) )
      | ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(126,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(746,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(825,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ B @ tc_nat ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

thf(1021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ B @ tc_nat ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(245,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(1042,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)],[245]) ).

thf(378,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ E ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ F ) ) )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_1) ).

thf(1355,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_List_Olist @ E ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ F ) ) )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(333,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(1255,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)],[333]) ).

thf(155,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(820,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)],[155]) ).

thf(442,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ A @ B @ C @ D @ E @ F ) @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_3) ).

thf(1487,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Osko__List__Xlist__all2__append1__1__1 @ A @ B @ C @ D @ E @ F ) @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ E ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(326,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(1238,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)],[326]) ).

thf(320,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(1223,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)],[320]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(894,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(317,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__hext_0) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).

thf(598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(788,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(384,axiom,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1370,plain,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(411,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).

thf(1423,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(241,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(1032,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)],[241]) ).

thf(382,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).

thf(1365,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(625,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
      = ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
      = ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(428,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(1457,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)],[428]) ).

thf(63,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(583,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ D )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_1) ).

thf(889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ D )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(493,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(396,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__def_0) ).

thf(1392,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(349,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).

thf(1291,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(217,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(974,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)],[217]) ).

thf(232,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).

thf(1012,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(274,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).

thf(1106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(195,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(916,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(11,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(467,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)],[11]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ 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(566,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(17,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(484,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(5,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(456,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(166,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(842,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)],[166]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
        = B )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__length01_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
        = B )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(340,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(1270,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)],[340]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

thf(1017,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(367,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).

thf(1328,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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(1064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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)],[255]) ).

thf(118,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(725,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)],[118]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

thf(980,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(412,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(1425,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)],[412]) ).

thf(287,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(1138,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)],[287]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).

thf(869,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(24,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(499,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)],[24]) ).

thf(398,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(1397,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)],[398]) ).

thf(380,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
        = A )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__length01_0) ).

thf(1360,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
        = A )
      | ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(33,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(519,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(61,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(578,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)],[61]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(697,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(267,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).

thf(1160,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != ( c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(129,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(753,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)],[129]) ).

thf(304,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(1182,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)],[304]) ).

thf(430,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XCallParams__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallParams_I2_J_1) ).

thf(1461,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XCallParams__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(96,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(669,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)],[96]) ).

thf(85,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(642,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)],[85]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(637,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(489,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).

thf(1214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(422,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWTs @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).

thf(1446,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWTs @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(314,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1207,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(293,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(1155,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)],[293]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Orotate @ B @ C @ D ) @ D )
      = ( c_List_Orotate @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).

thf(1028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Orotate @ B @ C @ D ) @ D )
      = ( c_List_Orotate @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

thf(1082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(365,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).

thf(1324,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(87,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(647,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)],[87]) ).

thf(222,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(985,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)],[222]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( hAPP @ ( c_List_Onth @ B @ C ) @ A )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).

thf(701,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( hAPP @ ( c_List_Onth @ B @ C ) @ A )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osize__class_Osize @ A @ ( 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__append_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(425,axiom,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_Us____ @ v_Ts____ @ tc_Type_Oty @ tc_Type_Oty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_I4_J_0) ).

thf(1451,plain,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_Us____ @ v_Ts____ @ tc_Type_Oty @ tc_Type_Oty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(391,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ E @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCons_0) ).

thf(1382,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ E @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(90,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(654,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)],[90]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(622,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(837,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(291,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ E )
        = ( hAPP @ ( c_List_Onth @ A @ D ) @ E ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).

thf(1150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ E )
        = ( hAPP @ ( c_List_Onth @ A @ D ) @ E ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(438,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconfs__conv__map__1__1 @ A @ C @ D @ E @ B ) @ C @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ D @ B ) @ E @ C @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__conv__map_1) ).

thf(1478,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconfs__conv__map__1__1 @ A @ C @ D @ E @ B ) @ C @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ D @ B ) @ E @ C @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).

thf(1266,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_lessequals @ C @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ D )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Oplus__class_Oplus @ A @ D @ tc_nat ) ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ D @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__drop_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ D )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Oplus__class_Oplus @ A @ D @ tc_nat ) ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ D @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(6,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(457,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).

thf(1333,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
      | ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).

thf(1434,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
      | ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(362,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_0) ).

thf(1318,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(312,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(1202,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(327,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(1241,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)],[327]) ).

thf(148,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(805,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)],[148]) ).

thf(91,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(657,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)],[91]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).

thf(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oreplicate @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D )
      = ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(433,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ E @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I15_J_0) ).

thf(1466,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ E @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).

thf(1026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(305,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(1185,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)],[305]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(98,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(674,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)],[98]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Oty_OClass @ A )
       != ( c_Type_Oty_OClass @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).

thf(773,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Oty_OClass @ A )
       != ( c_Type_Oty_OClass @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(794,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(93,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ H @ A @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ L @ B @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_3) ).

thf(662,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ H @ A @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ L @ B @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(116,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(718,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)],[116]) ).

thf(184,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(888,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)],[184]) ).

thf(192,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(906,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)],[192]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D )
        = ( c_List_Oappend @ ( c_List_Otake @ A @ C @ D ) @ ( c_List_Otake @ B @ ( c_List_Odrop @ A @ C @ D ) @ D ) @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__add_0) ).

thf(1135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D )
        = ( c_List_Oappend @ ( c_List_Otake @ A @ C @ D ) @ ( c_List_Otake @ B @ ( c_List_Odrop @ A @ C @ D ) @ D ) @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).

thf(1251,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(318,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(1219,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(440,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ A @ C @ B @ D @ E @ F ) @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ C @ B @ E ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_4) ).

thf(1483,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Osko__List__Xlist__all2__append1__1__2 @ A @ C @ B @ D @ E @ F ) @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ C @ B @ E ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(341,axiom,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1273,plain,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(172,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(856,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)],[172]) ).

thf(354,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ B @ C @ A @ D @ E @ F ) @ tc_Value_Oval ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ B @ C @ F ) @ A @ ( c_List_Olist_OCons @ D @ E @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_0) ).

thf(1301,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ B @ C @ A @ D @ E @ F ) @ tc_Value_Oval ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ B @ C @ F ) @ A @ ( c_List_Olist_OCons @ D @ E @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).

thf(573,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
        = D )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(689,plain,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(387,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCallNT_0) ).

thf(1374,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(562,plain,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__0_0) ).

thf(732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ 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(1125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ 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)],[282]) ).

thf(394,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).

thf(1388,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(179,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(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(210,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeRel_OMethod @ A @ B @ C @ D @ E @ F @ B @ G )
      | ~ ( c_TypeRel_OMethod @ A @ H @ C @ D @ E @ F @ B @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__idemp_0) ).

thf(958,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeRel_OMethod @ A @ B @ C @ D @ E @ F @ B @ G )
      | ~ ( c_TypeRel_OMethod @ A @ H @ C @ D @ E @ F @ B @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(230,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(1007,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)],[230]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ B @ ( c_List_Otake @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__drop_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ B @ ( c_List_Otake @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).

thf(1226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( B
        = ( c_List_Olist_OCons @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(47,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(545,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(202,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(936,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)],[202]) ).

thf(359,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(1312,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)],[359]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(268,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(1090,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)],[268]) ).

thf(206,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(947,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)],[206]) ).

thf(45,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(540,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)],[45]) ).

thf(97,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(672,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)],[97]) ).

thf(10,axiom,
    class_Power_Opower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(466,plain,
    class_Power_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(269,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 @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(1092,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 @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(334,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(1258,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)],[334]) ).

thf(111,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(704,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)],[111]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

thf(831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_nat )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(345,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(1282,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)],[345]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(1117,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
      = ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(444,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(1492,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)],[444]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1144,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(388,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_3) ).

thf(1376,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(301,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(1175,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)],[301]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(71,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(604,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)],[71]) ).

thf(101,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(681,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)],[101]) ).

thf(404,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ D @ C @ E )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ D @ E ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).

thf(1408,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ D @ C @ E )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ D @ E ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(1048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(123,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(736,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(181,axiom,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).

thf(880,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(88,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(649,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)],[88]) ).

thf(76,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(616,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)],[76]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Onat_Onat__case @ A @ B @ C @ D )
        = ( hAPP @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_1) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Onat_Onat__case @ A @ B @ C @ D )
        = ( hAPP @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).

thf(1080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(131,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(758,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)],[131]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).

thf(816,plain,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_1) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) )
        = ( hAPP @ ( c_List_Onth @ B @ C ) @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(67,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(594,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)],[67]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(34,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(520,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).

thf(964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
        = ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(350,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ D @ E ) @ C @ E )
      | ~ ( c_List_Olist__all2 @ A @ B @ D @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).

thf(1293,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ D @ E ) @ C @ E )
      | ~ ( c_List_Olist__all2 @ A @ B @ D @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(302,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(1177,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)],[302]) ).

thf(201,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(932,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)],[201]) ).

thf(159,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(827,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(256,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(1066,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

thf(780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(182,axiom,
    ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(883,plain,
    ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).

thf(1015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(277,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(1113,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)],[277]) ).

thf(273,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(1102,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)],[273]) ).

thf(27,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(505,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)],[27]) ).

thf(197,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(922,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)],[197]) ).

thf(194,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(912,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)],[194]) ).

thf(35,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(521,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)],[35]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

thf(1044,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(242,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(1034,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)],[242]) ).

thf(355,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ A @ B @ C @ D @ E @ F ) @ C @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_3) ).

thf(1304,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Osko__List__Xlist__all2__append2__1__1 @ A @ B @ C @ D @ E @ F ) @ C @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(65,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).

thf(589,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A
        = ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(40,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(531,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(409,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ v_C____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wte_0) ).

thf(1420,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ v_C____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(199,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(927,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)],[199]) ).

thf(343,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(1277,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)],[343]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(553,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
      = ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

thf(1076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( 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(939,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( 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)],[203]) ).

thf(372,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWTs @ A @ B @ ( c_List_Olist_OCons @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) )
      | ~ ( c_WellType_OWTs @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCons_0) ).

thf(1340,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWTs @ A @ B @ ( c_List_Olist_OCons @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) )
      | ~ ( c_WellType_OWTs @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

thf(458,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(157,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(823,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(62,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(580,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)],[62]) ).

thf(216,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(971,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)],[216]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ C ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) )
      = ( hAPP @ ( c_List_Onth @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length__plus_0) ).

thf(954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ C ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) )
      = ( hAPP @ ( c_List_Onth @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(114,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(712,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(52,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(557,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)],[52]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(1070,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(178,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).

thf(872,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( D
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(400,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).

thf(1400,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ D @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

thf(707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ B @ D @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1053,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Obutlast @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__butlast_0) ).

thf(1432,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Obutlast @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(426,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__hext_0) ).

thf(1452,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(791,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(64,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 )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(585,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 )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(26,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(502,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)],[26]) ).

thf(336,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(1262,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)],[336]) ).

thf(284,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(1130,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)],[284]) ).

thf(347,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(1285,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)],[347]) ).

thf(370,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_3) ).

thf(1336,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(265,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(1085,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)],[265]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(60,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(576,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)],[60]) ).

thf(379,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(1358,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)],[379]) ).

thf(125,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(744,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).

thf(1141,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
        = E )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(237,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(1023,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)],[237]) ).

thf(441,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts__wts_H_0) ).

thf(1485,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Otake @ A @ B @ C ) @ C )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_List_Otl @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__take_0) ).

thf(864,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Otake @ A @ B @ C ) @ C )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_List_Otl @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(413,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_0) ).

thf(1427,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( 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(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( 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)],[119]) ).

thf(385,axiom,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__CHAINED__1 @ v_E____ @ v_P @ v_Us____ @ v_es_Ha____ @ v_h_Ha____ ) @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).

thf(1372,plain,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__CHAINED__1 @ v_E____ @ v_P @ v_Us____ @ v_es_Ha____ @ v_h_Ha____ ) @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(74,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(612,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)],[74]) ).

thf(173,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(859,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)],[173]) ).

thf(319,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(1221,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(1284,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(377,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ D ) @ ( c_List_Orev @ C @ E ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).

thf(1353,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ D ) @ ( c_List_Orev @ C @ E ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(70,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(600,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)],[70]) ).

thf(270,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(1094,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)],[270]) ).

thf(219,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(978,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(167,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(845,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)],[167]) ).

thf(410,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_1) ).

thf(1421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(361,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ A @ B @ C @ D @ E @ F ) @ D @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_4) ).

thf(1316,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Osko__List__Xlist__all2__append2__1__2 @ A @ B @ C @ D @ E @ F ) @ D @ E @ F )
      | ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Oappend @ C @ D @ F ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).

thf(1459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(363,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_h_Ha____ @ v_E____ @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ v_C____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_I5_J_0) ).

thf(1321,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_h_Ha____ @ v_E____ @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ v_C____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(406,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(1412,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)],[406]) ).

thf(275,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(1108,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)],[275]) ).

thf(218,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(976,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)],[218]) ).

thf(191,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(903,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)],[191]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ D )
      = ( c_Nat_Onat_Onat__case @ A @ ( c_List_Onth @ B @ C ) @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth_Osimps_0) ).

thf(1189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ D )
      = ( c_Nat_Onat_Onat__case @ A @ ( c_List_Onth @ B @ C ) @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

thf(1010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(395,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(1390,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)],[395]) ).

thf(366,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I13_J_0) ).

thf(1326,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(212,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(961,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)],[212]) ).

thf(188,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ A @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ B @ L @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_2) ).

thf(896,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ A @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ B @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(332,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(1253,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)],[332]) ).

thf(109,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(699,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)],[109]) ).

thf(240,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(1030,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)],[240]) ).

thf(57,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(568,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)],[57]) ).

thf(95,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(667,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)],[95]) ).

thf(419,axiom,
    c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ ( v_sko__CHAINED__1 @ v_E____ @ v_P @ v_Us____ @ v_es_Ha____ @ v_h_Ha____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1440,plain,
    c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ ( v_sko__CHAINED__1 @ v_E____ @ v_P @ v_Us____ @ v_es_Ha____ @ v_h_Ha____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(357,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(1308,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)],[357]) ).

thf(309,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(1193,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)],[309]) ).

thf(189,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(899,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)],[189]) ).

thf(102,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(684,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)],[102]) ).

thf(43,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(536,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)],[43]) ).

thf(285,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(1133,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)],[285]) ).

thf(375,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ A @ B @ D @ E @ F @ C ) ) @ E ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_1) ).

thf(1348,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ A @ B @ D @ E @ F @ C ) ) @ E ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XIH__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IH_0) ).

thf(1280,plain,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XIH__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(322,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(1229,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)],[322]) ).

thf(397,axiom,
    ! [A: $i] :
      ( v_thesis____
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(1395,plain,
    ! [A: $i] :
      ( v_thesis____
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A @ v_Us____ @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ v_E____ @ v_es_Ha____ @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(390,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_2) ).

thf(1380,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(171,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(854,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)],[171]) ).

thf(330,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(1248,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)],[330]) ).

thf(439,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(1480,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)],[439]) ).

thf(162,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(833,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)],[162]) ).

thf(214,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(967,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)],[214]) ).

thf(207,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(950,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
        = A )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).

thf(1097,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
        = A )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(163,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(835,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).

thf(564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(417,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).

thf(1436,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

thf(801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
      | ~ ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(446,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
      | ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).

thf(1495,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
      | ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ A @ B @ ( hAPP @ ( c_List_Onth @ A @ C ) @ B ) @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).

thf(807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ A @ B @ ( hAPP @ ( c_List_Onth @ A @ C ) @ B ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(251,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(1056,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)],[251]) ).

thf(348,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(1288,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)],[348]) ).

thf(41,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(532,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(107,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

thf(696,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(297,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(1165,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)],[297]) ).

thf(144,axiom,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XCallParams__Xhyps__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallParams_Ohyps_I2_J_1) ).

thf(1363,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__XCallParams__Xhyps__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(360,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCall_0) ).

thf(1314,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(300,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(1172,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)],[300]) ).

thf(405,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCall @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G @ H @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellType_OWTs @ A @ B @ E @ G )
      | ~ ( c_TypeRel_OMethod @ A @ I @ D @ H @ F @ ( c_Pair @ J @ K @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ L @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ I ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCall_0) ).

thf(1410,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCall @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G @ H @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellType_OWTs @ A @ B @ E @ G )
      | ~ ( c_TypeRel_OMethod @ A @ I @ D @ H @ F @ ( c_Pair @ J @ K @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ L @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ I ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(134,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(767,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)],[134]) ).

thf(211,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(960,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)],[211]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ A @ B )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).

thf(1473,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ A @ B )
      = ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
        = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

thf(839,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
        = B )
      | ~ ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(124,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(740,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)],[124]) ).

thf(9,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(464,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)],[9]) ).

thf(339,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(1268,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)],[339]) ).

thf(392,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ C @ D ) @ E @ D )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ E ) @ C @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).

thf(1384,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ C @ D ) @ E @ D )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ E ) @ C @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(235,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(1019,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)],[235]) ).

thf(38,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(528,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( B
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).

thf(644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( B
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(225,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(992,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)],[225]) ).

thf(156,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(822,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(169,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(850,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(353,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ A @ B @ D @ E @ F @ C ) @ F @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_2) ).

thf(1299,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ A @ B @ D @ E @ F @ C ) @ F @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(105,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(691,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)],[105]) ).

thf(399,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_M____ @ v_esa____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_0) ).

thf(1399,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_OVal @ v_v____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_M____ @ v_esa____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(25,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(501,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(325,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(1236,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)],[325]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

thf(987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
      | ~ ( c_lessequals @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(68,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(596,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(389,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__widens_0) ).

thf(1378,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).

thf(982,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
       != ( 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(1004,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ B @ C @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_List_Osko__List__Xlist__all2__refl__1__1 @ A @ C ) ) @ ( c_List_Osko__List__Xlist__all2__refl__1__1 @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__refl_0) ).

thf(1331,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ B @ C @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_List_Osko__List__Xlist__all2__refl__1__1 @ A @ C ) ) @ ( c_List_Osko__List__Xlist__all2__refl__1__1 @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(147,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(803,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(383,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_2) ).

thf(1367,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(431,axiom,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XCallParams__Xhyps__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallParams_Ohyps_I2_J_0) ).

thf(1463,plain,
    ! [B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ v_P @ v_h_Ha____ @ A @ v_es_Ha____ @ ( v_sko__local__XCallParams__Xhyps__2__1 @ A @ v_P @ B @ v_es_Ha____ @ v_h_Ha____ ) )
      | ~ ( c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ A @ v_esa____ @ B )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ A @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(46,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(543,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)],[46]) ).

thf(53,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(560,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)],[53]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
       != ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(99,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(676,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(266,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1088,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(313,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).

thf(1204,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Oappend @ D @ E @ C ) )
      | ( B
        = ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
      | ( ( c_List_Olist_OCons @ A @ B @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(424,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I12_J_0) ).

thf(1449,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(66,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(592,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)],[66]) ).

thf(434,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).

thf(1468,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(258,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(1069,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1500,plain,
    $false,
    inference(e,[status(thm)],[892,1322,1036,809,1168,1454,479,1295,1110,481,909,628,777,555,1211,1158,1406,730,1443,994,449,878,614,861,1497,1078,533,550,715,1233,814,1260,1342,945,1063,538,930,829,1196,1001,709,1386,1475,651,1243,1127,782,1441,885,1046,570,1430,785,1264,619,751,1191,1147,770,1115,1100,969,606,448,1494,756,1373,1418,485,514,1051,1489,1415,492,1465,687,634,734,956,866,453,1119,660,998,1345,1405,507,527,1074,452,920,678,529,1438,925,1306,1199,1338,1470,1311,1067,1163,512,942,1153,761,1274,746,825,1021,1042,1355,1255,820,1487,1238,1223,894,1217,598,788,1370,1423,1032,1365,625,852,665,1457,583,889,461,493,1392,1291,974,1012,1106,916,467,847,566,484,456,842,1402,1270,1017,1328,1064,725,980,1425,1138,869,499,1397,1360,1350,519,578,697,1089,1160,753,1182,1461,669,642,637,489,1214,1446,1207,1039,1155,1028,1082,901,476,1324,647,985,701,1297,1451,1382,654,622,837,1150,1478,1266,1231,1060,457,1333,1434,1318,1202,1241,805,657,1170,1466,1026,1185,1187,674,773,794,662,718,888,906,1135,1251,1219,1483,1273,856,1301,573,689,1374,562,732,1125,1388,875,958,1007,694,1226,545,936,1312,1058,1090,947,540,672,466,1092,1258,704,831,1282,1117,990,1492,1144,1376,1175,764,604,681,1408,1048,736,509,880,649,616,1122,811,1080,631,758,816,609,594,799,520,964,1293,1177,932,827,1066,780,883,1015,1113,1102,505,922,912,521,1044,1245,722,1034,1304,589,531,548,1420,927,1277,749,516,553,473,1076,939,1340,458,823,580,971,954,712,557,1070,872,1400,707,1053,1432,1452,791,585,502,1262,1130,1285,1336,1085,470,576,1358,744,1141,1023,1485,864,1427,727,1372,612,859,1221,1284,1353,600,1094,978,845,1421,1316,1459,1180,1321,524,1412,1108,976,903,1448,1189,1010,1390,1326,961,896,1253,699,1030,568,667,1440,1308,1193,899,684,536,1133,1348,1280,1229,1395,818,1380,854,1248,1480,833,967,950,1097,835,564,1436,801,1495,807,1056,1288,532,696,1165,796,1363,1314,1172,1410,767,960,1473,839,740,464,1268,1384,1019,528,644,992,822,850,1299,691,1399,501,1236,987,596,1378,982,1004,1331,486,803,1367,1463,543,560,639,676,1088,1204,1449,592,1468,496,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV972-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n011.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 : Sun May 19 06:27:23 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.87/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.59/1.04  % [INFO] 	 Parsing done (200ms). 
% 1.59/1.05  % [INFO] 	 Running in sequential loop mode. 
% 2.21/1.26  % [INFO] 	 eprover registered as external prover. 
% 2.21/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 2.21/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.63/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 506 axioms. Running axiom selection ... 
% 3.10/1.49  % [INFO] 	 Axiom selection finished. Selected 445 axioms (removed 61 axioms). 
% 3.60/1.62  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.60/1.63  % [INFO] 	 Type checking passed. 
% 3.60/1.63  % [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 ... 
% 8.95/2.96  % External prover 'e' found a proof!
% 8.95/2.96  % [INFO] 	 Killing All external provers ... 
% 8.95/2.96  % Time passed: 2450ms (effective reasoning time: 1905ms)
% 8.95/2.96  % Axioms used in derivation (445): cls_butlast__snoc_0, cls_IH_0, cls_sees__method__fun_1, cls_add__0__left_0, cls_exp_Osimps_I9_J_1, cls_append__eq__append__conv__if_3, cls_nth__list__update__neq_0, cls_power__0_0, cls_widens__Cons_2, cls_rev__swap_1, cls_Nil__is__rev__conv_1, cls_list__all2__append1_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_calculation_I5_J_0, cls_take__eq__Nil_0, cls_Cons__eq__append__conv_2, cls_nth__Cons_H_0, cls_Cons__eq__append__conv_5, cls_nth__Cons__number__of_0, cls_le__diff__iff_0, cls_le__diff__conv_1, cls_list__all2__Cons_2, cls_eq__imp__le_0, cls_list__update__overwrite_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_list__all2__eq_1, cls_list__all2__append1_4, cls_append__self__conv_0, cls_drop__append_0, cls_zero__le__one_0, cls_take__0_0, cls_WTrtCallNT_0, cls_exp_Osimps_I81_J_0, cls_butlast_Osimps_I1_J_0, cls_eq__diff__iff_0, cls_replicate__empty_0, cls_tl_Osimps_I1_J_0, cls_take__Cons_H_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_rev__singleton__conv_1, cls_class__semiring_Osemiring__rules_I21_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_CHAINED_0, cls_power__increasing_0, cls_WTrt_H__WTrts_H_Ointros_I13_J_0, cls_add__le__cancel__left_1, cls_add__is__0_0, cls_not__Cons__self2_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_widen__Class_2, cls_WTs__implies__WTrts_0, cls_rev__is__rev__conv_0, cls_append__eq__append__conv__if_6, clsarity_nat__Orderings_Olinorder, cls_diff__cancel_0, cls_add__imp__eq_0, cls_add__le__cancel__right_1, cls_take__add_0, cls_list__all2__append2_1, cls_nth__Cons_H_1, cls_add__leE_0, cls_append__eq__Cons__conv_4, cls_COMBI__def__raw_0, cls_self__append__conv_0, cls_comm__monoid__add_Omult__1__right_0, cls_wts__wts_H_0, cls_drop__0_0, cls_list__update__nonempty_1, cls_add__diff__assoc2_0, cls_eq__Nil__appendI_0, cls_comm__monoid__add_Omult__assoc_0, cls_add__cancel__21_1, cls_ty_Osimps_I20_J_0, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_append__Cons_0, cls_confs__conv__map_1, cls_length__butlast_0, cls_CallParams_Ohyps_I2_J_1, cls_sees__method__fun_2, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_butlast_Osimps_I2_J_1, cls_le__0__eq_0, cls_rotate1__length01_0, cls_drop__Cons__number__of_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, cls_diff__diff__right_0, cls_diff__diff__left_0, cls_append__eq__Cons__conv_0, cls_nth_Osimps_0, cls_widens__trans_0, cls_one__le__power_0, cls_diff__le__mono2_0, cls_tl__replicate_0, cls_add__le__mono_0, cls_diff__diff__cancel_0, cls_butlast__list__update_0, cls_CallParams_I2_J_1, cls_of__nat__le__iff_1, cls_list__all2__append2_5, cls_append1__eq__conv_1, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_le__antisym_0, cls_add__right__mono_0, cls_order__eq__refl_0, cls_list__all2__rev_1, cls_power__0__left_0, cls_double__eq__0__iff_1, cls_widen__refl_0, cls_confs__Cons2_3, cls_right__minus__eq_0, cls_hext__trans_0, cls_of__nat__le__iff_0, cls_list__all2__rev_0, cls_list__all2__Cons_1, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_le__imp__diff__is__add_1, cls_hext__refl_0, cls_replicate__append__same_0, cls_list__update__beyond_0, cls_rev_Osimps_I2_J_0, cls_nth__via__drop_0, cls_take__1__Cons_0, cls_exp_Osimps_I9_J_0, cls_rev__singleton__conv_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_nth__append__length__plus_0, cls_add__nonneg__eq__0__iff_0, cls_append__Nil2_0, cls_nat_Osplit_0, cls_widens__refl_0, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_conf__widen_0, cls_append__self__conv2_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_CHAINED_1, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_add__left__mono_0, cls_self__append__conv2_0, cls_drop__tl_0, cls_Nitpick_Onat__case__def_1, cls_length__0__conv_0, cls_list__all2__append1_3, cls_self__append__conv2_1, cls_sees__method__fun_0, cls_WTrt__hext__mono_0, cls_append__eq__append__conv__if_4, cls_rotate__is__Nil__conv_0, cls_conf_0, cls_of__nat__0__le__iff_0, cls_Cons__eq__append__conv_3, cls_le__iff__diff__le__0_0, cls_rotate__rotate_0, cls_WTrt_H__WTrts_H_Ointros_I15_J_0, cls_append__is__Nil__conv_2, cls_diff__add__0_0, cls_length__list__update_0, cls_append__Nil_0, cls_class__semiring_Oadd__a_0, cls_append__eq__append__conv2_5, cls_wts_H__wts_0, cls_singleton__rev__conv_0, cls_append__eq__Cons__conv_5, cls_termination__basic__simps_I4_J_0, cls_trans__le__add1_0, cls_take__Cons_H_1, cls_of__nat__diff_0, cls_butlast__list__update_1, cls_drop__Cons__number__of_1, cls_termination__basic__simps_I3_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_butlast__conv__take_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_0, cls_rev__is__Nil__conv_0, cls_list__all2__Cons_0, cls_confs__Cons2_2, cls_replicate__app__Cons__same_0, cls_rotate__simps_0, cls_replicate__eq__replicate_1, cls_append__eq__Cons__conv_1, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_drop__1__Cons_0, cls_list__all2__refl_0, cls_add__cancel__21_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_rotate1__is__Nil__conv_0, cls_butlast__append_0, cls_list__all2__Nil_1, cls_self__append__conv_1, cls_take__append_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_list__update__code_I2_J_0, cls_list__all2__append2_4, cls_list__all2__appendI_0, cls_list__all2__append2_2, cls_rotate1__rotate__swap_0, cls_widens__Cons_0, cls_not__Cons__self_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_append__same__eq_0, cls_append__take__drop__id_0, cls_Nitpick_Onat__case__def_0, cls_zero__neq__one_0, cls_list__all2__def_0, cls_list__update__swap_0, cls_WTrtCall_0, cls_append__eq__conv__conj_0, cls_list__all2__rev1_1, cls_diff__self_0, cls_butlast__drop_0, cls_diff__is__0__eq_0, cls_natgb_Oadd__cancel_0, cls_drop__Cons_H_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_length__rev_0, cls_calculation_I4_J_0, cls_tl__take_0, cls_list__all2__append1_2, cls_drop__Nil_0, cls_append__assoc_0, cls_exp_Osimps_I80_J_0, cls_append__eq__append__conv__if_1, cls_add__diff__cancel_0, cls_butlast__append_1, cls_le__trans_0, cls_Pair__eq_0, cls_list__all2__Nil2_0, cls_Cons__eq__append__conv_0, cls_drop__butlast_0, cls_add__diff__assoc_0, cls_diff__add__assoc_0, cls_nat__add__right__cancel_0, cls_WT__implies__WTrt_0, cls_add__increasing_0, cls_ty_Oinject_0, cls_le__imp__diff__is__add_0, clsarity_nat__Orderings_Opreorder, cls_nat__diff__split__asm_1, cls_wt_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_right__minus__eq_1, cls_nat__diff__split_1, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_add__nonpos__nonpos_0, cls_diff__cancel2_0, cls_add__nonneg__eq__0__iff_1, cls_list__all2__dropI_0, cls_take__eq__Nil_2, cls_WTCons_0, cls_add__nonneg__nonneg_0, cls_empty__replicate_0, cls_append__eq__Cons__conv_2, cls_le__diff__conv_0, cls_le__diff__conv2_0, cls_replicate__add_0, cls_tl__append2_0, cls_list__all2__Nil_0, cls_rotate__simps_1, cls_rev__replicate_0, cls_drop__drop_0, cls_rev__eq__Cons__iff_1, clsarity_nat__Power_Opower, cls_drop__replicate_0, cls_conf__hext_0, cls_list__update__id_0, cls_nat__add__left__cancel__le_1, cls_Nat_Oadd__0__right_0, cls_eq__eqI_0, cls_nth__drop_0, cls_list_Osimps_I3_J_0, cls_rotate__is__Nil__conv_1, cls_le__add__diff__inverse_0, cls_le0_0, cls_list__all2__append2_3, cls_wt_H__wt_0, cls_le__eqI_0, cls_length__append_0, cls_le__add2_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_append__eq__conv__conj_1, cls_rev__is__Nil__conv_1, cls_list__all2__Cons1_3, cls_natgb_Oadd__r0__iff_0, cls_length__rotate1_0, cls_diff__self__eq__0_0, cls_ty_Osimps_I21_J_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_nat__add__left__cancel__le_0, cls_nth__Cons__number__of_1, cls_comm__monoid__add_Omult__left__commute_0, cls_list__all2__append1_5, cls_diff__0__right_0, cls_le__add__right__mono_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_confs__Cons2_1, cls_append__is__Nil__conv_1, cls_list__all2__append_0, cls_replicate__eq__replicate_2, cls_length__rotate_0, cls_confs__Cons2_0, cls_widens__Cons_1, cls_widen__trans_0, cls_diff__le__self_0, cls_list__all2__takeI_0, cls_diff__add__assoc2_0, cls_le__diff__conv2_1, cls_length__tl_0, cls_nat__le__linear_0, cls_WTrts__hext__mono_0, cls_Nil__is__rev__conv_0, cls_plus__nat_Oadd__0_0, cls_comm__monoid__add_Omult__1_0, cls_length__drop_0, cls_confs__widens_0, cls_list__all2__append_2, cls_exp_Osimps_I9_J_2, cls_Cons__eq__appendI_0, cls_WTrtCons_0, cls_confs__hext_0, cls_list__all2__append1_1, cls_WTrt_H__WTrts_H_Ointros_I12_J_0, cls_append__is__Nil__conv_0, cls_add__nonneg__eq__0__iff_2, cls_eq__eqI_1, cls_class__semiring_Oadd__c_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_nat__add__left__cancel_0, cls_add__le__mono1_0, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_append__eq__append__conv__if_0, cls_le__iff__add_1, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_add__is__0_2, cls_sees__method__fun_3, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_append__eq__appendI_0, cls_wtes_0, cls_wte_0, cls_rotate__length01_0, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_le__diff__iff_1, cls_rev__append_0, cls_butlast__take_0, cls_Cons__eq__append__conv_1, cls_take__Cons__number__of_0, cls_drop__take_0, cls_take__all_0, cls_WTCall_0, cls_sees__method__idemp_0, cls_add__mono_0, cls_Nil__is__append__conv_2, cls_nth__append__length_0, cls_diff__add__inverse_0, cls_diffs0__imp__equal_0, cls_rev__swap_0, cls_eq__iff__diff__eq__0_1, cls_tl__drop_0, cls_replicate__empty_1, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_class__semiring_Osemiring__rules_I24_J_0, cls_list__all2__eq_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_tl_Osimps_I2_J_0, cls_wt__wt_H_0, cls_diff__le__mono_0, cls_zero__le__power_0, cls_rev__eq__Cons__iff_0, cls_list__all2__append2_0, cls_take__drop_0, cls_add__leE_1, cls_that_0, cls_le__eqI_1, cls_class__semiring_Opwr__0_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_nat__case__0_0, cls_le__iff__diff__le__0_1, cls_monoid__add__class_Oadd__0__right_0, cls_diff__commute_0, cls_le__add1_0, cls_drop__all_0, cls_le__add__diff_0, cls_drop__eq__Nil_0, cls_append__eq__Cons__conv_3, cls_eq__iff__diff__eq__0_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_COMBI__def_0, cls_widens__Cons_3, cls_Pair__eq_1, cls_rev__rev__ident_0, cls_add__le__cancel__left_0, cls_empty__replicate_1, cls_list_Osimps_I2_J_0, cls_power__decreasing_0, cls_zero__le__imp__of__nat_0, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_CallParams_I2_J_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_le__refl_0, cls_CallParams_Ohyps_I2_J_0, cls_power__0__left_1, cls_list__all2__append_1, cls_add__le__cancel__right_0, cls_exp_Osimps_I3_J_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_list__update__nonempty_0, cls_IH_1, cls_power__mono_0, cls_list__all2__rev1_0
% 8.95/2.96  % No. of inferences in proof: 895
% 8.95/2.97  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2450 ms resp. 1905 ms w/o parsing
% 9.76/3.13  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.76/3.13  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------