%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET818-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:54:23 EDT 2023

% Result   : Unsatisfiable 10.34s 3.39s
% Output   : Refutation 11.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1331
% Syntax   : Number of formulae    : 2500 ( 387 unt; 163 typ;   0 def)
%            Number of atoms       : 4385 ( 268 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 13178 (2066   ~;2048   |;   0   &;9064   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  326 ( 326   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  165 ( 163 usr;  11 con; 0-6 aty)
%            Number of variables   : 3170 (   0   ^;3170   !;   0   ?;3170   :)

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

thf(v_x_type,type,
    v_x: $i > $i ).

thf(tc_IntDef_Oint_type,type,
    tc_IntDef_Oint: $i ).

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

thf(c_0_type,type,
    c_0: $i ).

thf(c_Wellfounded__Recursion_Owf_type,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

thf(c_Wellfounded__Relations_Oless__than_type,type,
    c_Wellfounded__Relations_Oless__than: $i ).

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

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

thf(c_append_type,type,
    c_append: $i > $i > $i > $i ).

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

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

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

thf(c_List_Olistrel_type,type,
    c_List_Olistrel: $i > $i > $i ).

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

thf(c_emptyset_type,type,
    c_emptyset: $i ).

thf(c_Datatype__Universe_OIn1_type,type,
    c_Datatype__Universe_OIn1: $i > $i > $i > $i ).

thf(c_Datatype__Universe_OIn0_type,type,
    c_Datatype__Universe_OIn0: $i > $i > $i > $i ).

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

thf(c_SetInterval_OlessThan_type,type,
    c_SetInterval_OlessThan: $i > $i > $i ).

thf(c_Wellfounded__Recursion_Oacyclic_type,type,
    c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).

thf(c_Relation_Oconverse_type,type,
    c_Relation_Oconverse: $i > $i > $i > $i ).

thf(c_Nat_Osize_type,type,
    c_Nat_Osize: $i > $i > $i ).

thf(c_SetInterval_OgreaterThan_type,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

thf(c_List_Olex_type,type,
    c_List_Olex: $i > $i > $i ).

thf(c_Datatype__Universe_Odprod_type,type,
    c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(tc_Datatype__Universe_Onode_type,type,
    tc_Datatype__Universe_Onode: $i > $i > $i ).

thf(c_Datatype__Universe_OScons_type,type,
    c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__1_type,type,
    c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__2_type,type,
    c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__3_type,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__4_type,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

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

thf(class_HOL_Otimes_type,type,
    class_HOL_Otimes: $i > $o ).

thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

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

thf(class_Ring__and__Field_Opordered__cancel__comm__semiring_type,type,
    class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).

thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

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

thf(class_Ring__and__Field_Osemiring_type,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

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

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

thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

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

thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_type,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
    class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).

thf(class_HOL_Oplus_type,type,
    class_HOL_Oplus: $i > $o ).

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

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

thf(class_Ring__and__Field_Olordered__ring_type,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

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

thf(c_List_Olists_type,type,
    c_List_Olists: $i > $i > $i ).

thf(class_Orderings_Oord_type,type,
    class_Orderings_Oord: $i > $o ).

thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

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

thf(class_Ring__and__Field_Opordered__ring_type,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

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

thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(c_uminus_type,type,
    c_uminus: $i > $i > $i ).

thf(class_Power_Orecpower_type,type,
    class_Power_Orecpower: $i > $o ).

thf(class_Ring__and__Field_Osemiring__1__cancel_type,type,
    class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).

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

thf(class_Ring__and__Field_Ocomm__semiring__0_type,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

thf(c_Finite__Set_OFinites_type,type,
    c_Finite__Set_OFinites: $i ).

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Ocomm__semiring__0__cancel_type,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

thf(class_Numeral_Onumber__ring_type,type,
    class_Numeral_Onumber__ring: $i > $o ).

thf(class_Ring__and__Field_Osemiring__0__cancel_type,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

thf(c_SetInterval_OatLeastAtMost_type,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
    class_OrderedGroup_Olordered__ab__group__join: $i > $o ).

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

thf(class_HOL_Ominus_type,type,
    class_HOL_Ominus: $i > $o ).

thf(c_less_type,type,
    c_less: $i > $i > $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__meet_type,type,
    class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).

thf(class_LOrder_Ojoin__semilorder_type,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

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

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

thf(c_SetInterval_OgreaterThanAtMost_type,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

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

thf(class_OrderedGroup_Osemigroup__mult_type,type,
    class_OrderedGroup_Osemigroup__mult: $i > $o ).

thf(c_Divides_Oop_Advd_type,type,
    c_Divides_Oop_Advd: $i > $i > $i > $o ).

thf(c_GCD_Ogcd_type,type,
    c_GCD_Ogcd: $i > $i ).

thf(class_HOL_Ozero_type,type,
    class_HOL_Ozero: $i > $o ).

thf(class_Ring__and__Field_Oring_type,type,
    class_Ring__and__Field_Oring: $i > $o ).

thf(class_LOrder_Omeet__semilorder_type,type,
    class_LOrder_Omeet__semilorder: $i > $o ).

thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_type,type,
    class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).

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

thf(class_Ring__and__Field_Ocomm__semiring_type,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

thf(c_union_type,type,
    c_union: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

thf(class_LOrder_Olorder_type,type,
    class_LOrder_Olorder: $i > $o ).

thf(c_SetInterval_OatLeastLessThan_type,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_times_type,type,
    c_times: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

thf(class_HOL_Oone_type,type,
    class_HOL_Oone: $i > $o ).

thf(c_SetInterval_OatLeast_type,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(c_plus_type,type,
    c_plus: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Ocomm__ring_type,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

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

thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(c_Pow_type,type,
    c_Pow: $i > $i > $i ).

thf(class_Ring__and__Field_Opordered__semiring_type,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(class_Nat_Opower_type,type,
    class_Nat_Opower: $i > $o ).

thf(c_Relation_Orel__comp_type,type,
    c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).

thf(c_SetInterval_OatMost_type,type,
    c_SetInterval_OatMost: $i > $i > $i ).

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

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

thf(c_minus_type,type,
    c_minus: $i > $i > $i > $i ).

thf(c_UNIV_type,type,
    c_UNIV: $i ).

thf(class_OrderedGroup_Olordered__ab__group_type,type,
    class_OrderedGroup_Olordered__ab__group: $i > $o ).

thf(c_Datatype__Universe_Odsum_type,type,
    c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).

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

thf(class_Ring__and__Field_Oaxclass__abs__if_type,type,
    class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).

thf(c_Relation_OId_type,type,
    c_Relation_OId: $i ).

thf(c_Relation_OImage_type,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(c_Sum__Type_OInr_type,type,
    c_Sum__Type_OInr: $i > $i > $i > $i ).

thf(c_Sum__Type_OInl_type,type,
    c_Sum__Type_OInl: $i > $i > $i > $i ).

thf(c_inter_type,type,
    c_inter: $i > $i > $i > $i ).

thf(class_Parity_Oeven__odd_type,type,
    class_Parity_Oeven__odd: $i > $o ).

thf(class_Numeral_Onumber_type,type,
    class_Numeral_Onumber: $i > $o ).

thf(c_Transitive__Closure_Otrancl_type,type,
    c_Transitive__Closure_Otrancl: $i > $i > $i ).

thf(c_Transitive__Closure_Ortrancl_type,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(c_IntDef_Oint_type,type,
    c_IntDef_Oint: $i > $i ).

thf(c_Main_OImageE__1_type,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Relation_Odiag_type,type,
    c_Relation_Odiag: $i > $i > $i ).

thf(c_Sum__Type_OPlus_type,type,
    c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).

thf(tc_sum_type,type,
    tc_sum: $i > $i > $i ).

thf(c_Main_OPlusE__1_type,type,
    c_Main_OPlusE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OPlusE__2_type,type,
    c_Main_OPlusE__2: $i > $i > $i > $i > $i ).

thf(c_Datatype__Universe_Ouprod_type,type,
    c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).

thf(c_SetInterval_OgreaterThanLessThan_type,type,
    c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).

thf(c_Datatype_Ooption_OSome_type,type,
    c_Datatype_Ooption_OSome: $i > $i > $i ).

thf(class_Divides_Odiv_type,type,
    class_Divides_Odiv: $i > $o ).

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

thf(c_Union_type,type,
    c_Union: $i > $i > $i ).

thf(c_Main_OUnionE__1_type,type,
    c_Main_OUnionE__1: $i > $i > $i > $i ).

thf(c_Relation_ORange_type,type,
    c_Relation_ORange: $i > $i > $i > $i ).

thf(c_Main_ORangeE__1_type,type,
    c_Main_ORangeE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OsubsetI__1_type,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_Main_OconverseE__1_type,type,
    c_Main_OconverseE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OconverseE__2_type,type,
    c_Main_OconverseE__2: $i > $i > $i > $i > $i ).

thf(c_Main_Oin__listsI__1_type,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

thf(c_Inter_type,type,
    c_Inter: $i > $i > $i ).

thf(c_Main_OInterI__1_type,type,
    c_Main_OInterI__1: $i > $i > $i > $i ).

thf(c_Main_OuprodE__1_type,type,
    c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OuprodE__2_type,type,
    c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Datatype_Oo2s_type,type,
    c_Datatype_Oo2s: $i > $i > $i ).

thf(c_Infinite__Set_Oatmost__one_type,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(c_Main_Orel__compE__1_type,type,
    c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_Orel__compE__3_type,type,
    c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).

thf(c_1_type,type,
    c_1: $i ).

thf(c_Main_Ofinite__Union__1_type,type,
    c_Main_Ofinite__Union__1: $i > $i > $i ).

thf(c_Main_OdiagE__1_type,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(c_Main_Orel__compE__2_type,type,
    c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_OIdE__1_type,type,
    c_Main_OIdE__1: $i > $i > $i ).

thf(c_Divides_Oop_Amod_type,type,
    c_Divides_Oop_Amod: $i > $i > $i > $i ).

thf(c_Main_Omod__eq__0D__dest__1_type,type,
    c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).

thf(c_Main_Ozmod__eq__0D__dest__1_type,type,
    c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).

thf(c_Relation_ODomain_type,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(c_Main_ODomainE__1_type,type,
    c_Main_ODomainE__1: $i > $i > $i > $i > $i ).

thf(494,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).

thf(2163,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(240,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

thf(1665,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

thf(2630,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(156,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
      | ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(1501,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
      | ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

thf(2094,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

thf(1767,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

thf(1559,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(1002,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).

thf(3167,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(878,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

thf(2921,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

thf(1840,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(1179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

thf(1818,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).

thf(1549,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(2280,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(538,axiom,
    class_OrderedGroup_Osemigroup__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(2250,plain,
    class_OrderedGroup_Osemigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).

thf(1879,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

thf(1337,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).

thf(1718,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(719,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

thf(2612,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

thf(3053,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(1112,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ A @ c_1 @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).

thf(3345,plain,
    ! [A: $i] :
      ( ~ ( c_less @ A @ c_1 @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(585,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

thf(2341,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(582,axiom,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(2336,plain,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).

thf(2109,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

thf(2131,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).

thf(1454,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

thf(2031,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(1144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(3399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(409,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

thf(1995,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

thf(2412,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

thf(2876,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

thf(2463,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

thf(1899,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

thf(2787,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(711,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

thf(2595,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(335,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

thf(1850,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(663,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).

thf(2499,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

thf(2427,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).

thf(1982,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).

thf(2077,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(1011,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
      | ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(3185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
      | ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OlessThan @ B @ A )
       != ( c_SetInterval_OlessThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(1211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OlessThan @ B @ A )
       != ( c_SetInterval_OlessThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(569,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

thf(2309,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(953,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(3072,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

thf(1290,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

thf(2527,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

thf(1401,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(966,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(3098,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(749,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(2671,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(925,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
      | ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(3012,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
      | ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

thf(1305,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

thf(1437,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(1132,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(3382,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Nat_Opower @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(2117,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Nat_Opower @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).

thf(2940,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

thf(1596,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

thf(2231,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(2622,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(735,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).

thf(2644,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(661,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
      | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(2495,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
      | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(1039,axiom,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(3230,plain,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

thf(2381,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

thf(2395,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(443,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != c_emptyset )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(2062,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != c_emptyset )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(802,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(2776,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(1155,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

thf(3417,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).

thf(1618,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1072,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
      | ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(3285,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
      | ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).

thf(1569,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

thf(2248,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).

thf(1728,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(971,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

thf(3108,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

thf(2099,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

thf(2282,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).

thf(1591,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(1971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).

thf(1793,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(1146,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(3402,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(2854,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).

thf(1533,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(1173,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)],[4]) ).

thf(148,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).

thf(1486,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
      | ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(1608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
      | ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

thf(1655,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(942,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
       != ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(3049,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
       != ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

thf(1310,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1121,axiom,
    class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

thf(3365,plain,
    class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).

thf(1735,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).

thf(1999,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(66,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
       != ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(1327,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
       != ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(868,axiom,
    ! [A: $i] :
      ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(2901,plain,
    ! [A: $i] :
      ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

thf(2042,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

thf(2146,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

thf(1458,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(118,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

thf(1426,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(1031,axiom,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(3217,plain,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(717,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(2607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(756,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).

thf(2686,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(1105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(3332,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(1123,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(3367,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(343,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

thf(1867,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(1006,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

thf(3175,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(1108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(3338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(884,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

thf(2933,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(1275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(483,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(2141,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(369,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

thf(1919,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(1056,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(3253,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(405,axiom,
    class_HOL_Otimes @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(1988,plain,
    class_HOL_Otimes @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(645,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

thf(2459,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

thf(1761,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

thf(1342,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(978,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).

thf(3121,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).

thf(1507,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(1222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(594,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

thf(2360,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(1067,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(3276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(701,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

thf(2575,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(1125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(3370,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(1043,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(3236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

thf(2046,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatLeast @ B @ A )
       != ( c_SetInterval_OatLeast @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatLeast @ B @ A )
       != ( c_SetInterval_OatLeast @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(961,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

thf(3088,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

thf(1366,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

thf(2531,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

thf(1887,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(897,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(2957,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

thf(2985,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

thf(2227,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(1645,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

thf(1921,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(860,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

thf(2886,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

thf(1359,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

thf(1386,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(1070,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).

thf(3281,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(988,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).

thf(3140,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).

thf(1724,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(615,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

thf(2400,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).

thf(1967,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).

thf(2067,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(829,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).

thf(2825,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(826,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

thf(2819,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

thf(1803,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
     != ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(1228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
     != ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(1482,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(1254,plain,
    ! [A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(1024,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(3204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).

thf(2603,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(1160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(3425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).

thf(2339,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

thf(1871,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).

thf(2217,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

thf(2654,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

thf(1628,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(1018,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(3195,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(933,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

thf(3029,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

thf(2735,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

thf(2814,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(762,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(2698,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(983,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

thf(3131,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).

thf(1298,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(975,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(3116,plain,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(747,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).

thf(2667,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(363,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).

thf(1907,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(664,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

thf(2501,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).

thf(1323,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(992,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(3148,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).

thf(1511,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

thf(2274,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

thf(2682,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(980,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

thf(3125,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

thf(1826,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(1151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(3410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).

thf(2185,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

thf(1577,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).

thf(1832,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(866,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

thf(2897,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ B @ A @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ B @ A @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(136,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).

thf(1462,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(939,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(3043,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(786,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).

thf(2745,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(699,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(2571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).

thf(1545,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(758,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

thf(2691,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).

thf(2713,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(497,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

thf(2169,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(1030,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(3216,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

thf(2929,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(926,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).

thf(3014,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

thf(1641,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

thf(1773,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(1875,plain,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(1063,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(3268,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(831,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).

thf(2829,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(1127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ D @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(3374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(1134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(3385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(1247,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

thf(2552,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

thf(1319,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(261,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).

thf(1704,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(601,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

thf(2373,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

thf(1347,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(280,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).

thf(1741,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

thf(1398,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(959,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).

thf(3084,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1090,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
      | ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(3312,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
      | ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(375,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(1931,plain,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(191,axiom,
    class_HOL_Oone @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(1568,plain,
    class_HOL_Oone @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).

thf(2301,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

thf(1494,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(913,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

thf(2989,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(1362,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

thf(1963,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).

thf(2852,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(1040,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(3231,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(608,axiom,
    ! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(2388,plain,
    ! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

thf(2533,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

thf(2007,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(1096,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(3322,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(1164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
      | ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(3431,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
      | ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(916,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(2996,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(543,axiom,
    class_Numeral_Onumber @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(2259,plain,
    class_Numeral_Onumber @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(641,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(2451,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(1116,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(3357,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

thf(1581,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

thf(2017,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

thf(2178,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(2222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

thf(2950,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(531,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

thf(2237,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).

thf(1415,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

thf(2616,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

thf(1946,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(138,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).

thf(1465,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

thf(2794,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).

thf(1714,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

thf(2027,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

thf(2105,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(315,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(1811,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(130,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(1450,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).

thf(2090,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(1139,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(3393,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

thf(1911,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(1079,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(3295,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(864,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).

thf(2893,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

thf(1632,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(650,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

thf(2469,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1000,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

thf(3163,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

thf(2650,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(857,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

thf(2880,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(250,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).

thf(1682,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

thf(1828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(2925,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(247,axiom,
    class_HOL_Ozero @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(1677,plain,
    class_HOL_Ozero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(429,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(2034,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(1075,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(3290,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(1083,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ( A
        = ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(3300,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ( A
        = ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

thf(2777,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(994,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

thf(3152,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ A @ c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(1183,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ A @ c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).

thf(2073,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(900,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(2964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).

thf(2058,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_in @ ( v_x @ A ) @ A @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1169,plain,
    ! [A: $i] : ( c_in @ ( v_x @ A ) @ A @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(634,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).

thf(2437,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(951,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

thf(3068,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(722,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

thf(2618,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(1158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
      | ( B
        = ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(3421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
      | ( B
        = ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(656,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

thf(2483,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).

thf(2523,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(1622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).

thf(1351,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).

thf(1600,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(859,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

thf(2884,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

thf(2762,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

thf(1394,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

thf(2772,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(169,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).

thf(1526,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

thf(2137,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(1119,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
      | ( A
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(3361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
      | ( A
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(1048,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(3243,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(820,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).

thf(2809,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(1345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(815,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

thf(2799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(557,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(2286,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(1101,axiom,
    class_HOL_Oone @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(3327,plain,
    class_HOL_Oone @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(122,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).

thf(1433,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(464,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

thf(2103,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(789,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).

thf(2750,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(107,axiom,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

thf(1405,plain,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(1036,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(3226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(1201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

thf(1697,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(1242,plain,
    ! [B: $i,A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1028,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(3211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(166,axiom,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).

thf(1521,plain,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(1149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(3406,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(2205,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(398,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).

thf(1975,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).

thf(1564,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1604,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).

thf(2011,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(1038,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(3229,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(924,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(3011,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(1084,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(3303,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(652,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

thf(2473,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).

thf(1691,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).

thf(2364,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(1094,axiom,
    class_HOL_Ozero @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(3318,plain,
    class_HOL_Ozero @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(1156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
      | ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(3418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
      | ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(341,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

thf(1863,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(1166,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(3435,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(895,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(2954,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

thf(1651,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

thf(3169,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(1062,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( A
        = ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(3265,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( A
        = ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

thf(2646,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

thf(1915,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

thf(1708,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

thf(1783,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(782,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

thf(2737,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(562,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

thf(2296,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(568,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(2307,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

thf(2083,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

thf(2790,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

thf(2660,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

thf(2905,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(274,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(1730,plain,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(937,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(3037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(2589,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

thf(2264,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(714,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

thf(2601,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

thf(2541,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(165,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).

thf(1519,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(80,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(1355,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(902,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

thf(2969,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(1045,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(3239,plain,
    class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).

thf(2015,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

thf(1883,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(2441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).

thf(2673,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

thf(2733,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(693,axiom,
    c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(2560,plain,
    c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

thf(2805,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(246,axiom,
    class_Nat_Opower @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(1676,plain,
    class_Nat_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

thf(2133,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(930,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatMost @ B @ A )
       != ( c_SetInterval_OatMost @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(3022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatMost @ B @ A )
       != ( c_SetInterval_OatMost @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

thf(1751,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(1041,axiom,
    class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

thf(3233,plain,
    class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(886,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

thf(2937,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(995,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

thf(3154,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(985,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

thf(3134,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(322,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

thf(1824,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

thf(2150,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

thf(1370,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).

thf(2890,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(622,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

thf(2414,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(1053,axiom,
    class_Orderings_Olinorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(3250,plain,
    class_Orderings_Olinorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(208,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

thf(1602,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(727,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

thf(2628,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1081,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(3297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).

thf(1296,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

thf(1687,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semidom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

thf(1624,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(513,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

thf(2200,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(990,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).

thf(3144,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

thf(2345,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(518,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

thf(2211,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(784,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).

thf(2741,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

thf(1573,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(1071,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(3282,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

thf(2958,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(116,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(1423,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(1087,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(3307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(1064,axiom,
    class_Nat_Opower @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(3271,plain,
    class_Nat_Opower @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(638,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

thf(2445,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(1015,axiom,
    class_Ring__and__Field_Oidom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).

thf(3191,plain,
    class_Ring__and__Field_Oidom @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).

thf(1938,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

thf(2758,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(632,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ c_emptyset @ C )
        = ( c_insert @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(2433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ c_emptyset @ C )
        = ( c_insert @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(654,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

thf(2477,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(962,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(3090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(696,axiom,
    class_LOrder_Olorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(2565,plain,
    class_LOrder_Olorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(1020,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(3198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(745,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

thf(2663,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).

thf(1555,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

thf(2332,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(1091,axiom,
    class_Orderings_Oord @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(3314,plain,
    class_Orderings_Oord @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(853,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(2872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

thf(1951,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

thf(1836,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

thf(1787,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

thf(2181,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(578,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(2327,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(519,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(2213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(687,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).

thf(2547,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

thf(2313,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(224,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(1634,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

thf(1392,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(935,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

thf(3033,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1150,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(3408,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(969,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(3105,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(387,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

thf(1953,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(865,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

thf(2895,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

thf(2841,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

thf(2973,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(768,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

thf(2709,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(760,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

thf(2694,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(348,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(1878,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(977,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(3119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(956,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

thf(3078,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).

thf(1755,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(732,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Numeral_Onumber @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

thf(2638,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Numeral_Onumber @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

thf(2268,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

thf(3001,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

thf(2245,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(378,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

thf(1936,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(1234,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

thf(1541,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

thf(2157,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(470,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(2115,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(671,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

thf(2515,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(1057,axiom,
    class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).

thf(3254,plain,
    class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != B )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(1259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != B )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(891,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

thf(2946,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

thf(2377,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(816,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).

thf(2801,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(702,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(2577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(1131,axiom,
    class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

thf(3381,plain,
    class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).

thf(1498,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).

thf(1587,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

thf(2509,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(3102,plain,
    ! [A: $i] :
      ( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(244,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

thf(1672,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(775,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(2724,plain,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(846,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(2858,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(682,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

thf(2537,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(947,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(3060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

thf(3018,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(814,axiom,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(2798,plain,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(1089,axiom,
    class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

thf(3311,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(84,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ B @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

thf(1361,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

thf(1292,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(7,axiom,
    ! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1182,plain,
    ! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

thf(2868,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

thf(2419,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(354,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

thf(1889,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

thf(2023,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(1100,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(3326,plain,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(381,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

thf(1942,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).

thf(1659,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

thf(2323,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(1008,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

thf(3179,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(694,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).

thf(2561,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(1027,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(3210,plain,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(964,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(3094,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

thf(1739,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

thf(1424,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).

thf(2455,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

thf(2196,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(1842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(305,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

thf(1791,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
      | ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(3428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
      | ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(18,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(1214,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(589,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

thf(2349,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).

thf(2038,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

thf(1446,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(689,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(2551,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

thf(2085,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

thf(1612,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).

thf(2978,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

thf(2317,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(1078,axiom,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(3294,plain,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(805,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

thf(2781,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

thf(1419,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

thf(2125,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(753,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(2681,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(534,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
      | ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(2243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
      | ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(1984,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

thf(1852,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(792,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

thf(2756,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(1759,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).

thf(2370,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

thf(1478,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OgreaterThan @ B @ A )
       != ( c_SetInterval_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OgreaterThan @ B @ A )
       != ( c_SetInterval_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(673,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

thf(2519,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(171,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(1530,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

thf(1539,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(835,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oidom @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).

thf(2836,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oidom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).

thf(1456,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(1382,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(658,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).

thf(2487,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(839,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

thf(2845,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(1266,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(3354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(2355,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).

thf(1932,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(704,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).

thf(2581,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(648,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(2465,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(666,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

thf(2505,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(1137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(3390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1033,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
      | ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(3222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
      | ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(662,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

thf(2497,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(697,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(2566,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)],[697]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

thf(1799,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(120,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

thf(1429,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1052,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( A
        = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(3247,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( A
        = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

thf(2862,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).

thf(2766,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

thf(2052,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(949,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

thf(3064,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

thf(1720,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(1979,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

thf(3074,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(921,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

thf(3005,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

thf(2272,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1120,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(3364,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).

thf(1333,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).

thf(1991,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(764,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(2702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).

thf(1779,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(257,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

thf(1695,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

thf(3173,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ~ ( c_lessequals @ ( v_x @ A ) @ c_0 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1170,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( v_x @ A ) @ c_0 @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).

thf(2402,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).

thf(2915,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(1515,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).

thf(1895,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(872,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

thf(2909,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(730,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

thf(2634,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(788,axiom,
    class_HOL_Oplus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(2749,plain,
    class_HOL_Oplus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

thf(1857,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

thf(1814,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1035,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(3225,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(1069,axiom,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(3279,plain,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(1010,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

thf(3183,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).

thf(1712,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(1846,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).

thf(1286,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

thf(2368,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(619,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(2408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

thf(1663,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1014,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(3190,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

thf(2189,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(215,axiom,
    ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(1616,plain,
    ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(744,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(2662,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(1185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).

thf(2423,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(678,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).

thf(2529,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).

thf(1278,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(778,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(2729,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

thf(2001,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

thf(2292,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(706,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).

thf(2585,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

thf(1927,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1061,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
      | ~ ( c_in @ C @ A @ B )
      | ~ ( c_in @ D @ A @ B )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(3262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
      | ~ ( c_in @ C @ A @ B )
      | ~ ( c_in @ D @ A @ B )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(1066,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(3274,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
      | ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

thf(1374,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(1142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(3396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).

thf(2121,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

thf(2235,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).

thf(2144,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(752,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Sum__Type_OInr @ A @ B @ C )
       != ( c_Sum__Type_OInr @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(2677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Sum__Type_OInr @ A @ B @ C )
       != ( c_Sum__Type_OInr @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

thf(2176,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

thf(2391,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

thf(1680,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

thf(1959,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(692,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(2556,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)],[692]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(2253,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(428,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(2033,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(1059,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(3257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(772,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( A
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
      | ( A
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(2717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( A
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
      | ( A
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(1219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(698,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(2570,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(283,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(1747,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(1110,axiom,
    class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).

thf(3343,plain,
    class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(997,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(3158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(544,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).

thf(2260,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(1126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(3372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(1095,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
      | ( A
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(3319,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
      | ( A
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(525,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

thf(2225,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(1058,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(3255,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(1046,axiom,
    class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

thf(3240,plain,
    class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(809,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(2789,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(676,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).

thf(2525,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(909,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

thf(2981,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).

thf(1929,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

thf(1403,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

thf(1965,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).

thf(2827,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(1029,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(3213,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(1135,axiom,
    class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(3387,plain,
    class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(1012,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(3187,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(952,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

thf(3070,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(777,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).

thf(2727,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(1042,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
      | ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(3234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
      | ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(436,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

thf(2048,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(1620,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(659,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(2489,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

thf(2393,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

thf(3086,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).

thf(1388,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(1065,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(3272,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(1535,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
      | ( c_less @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(914,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Olordered__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

thf(2991,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Olordered__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

thf(1795,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(1147,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(3404,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(825,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(2817,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != c_0 )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(1256,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != c_0 )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).

thf(1488,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

thf(2161,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).

thf(1503,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(242,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(1669,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

thf(2220,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).

thf(2029,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
       != ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(1271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
       != ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

thf(1312,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1103,axiom,
    class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(3330,plain,
    class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(979,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).

thf(3123,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(1167,axiom,
    c_less @ c_0 @ c_1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

thf(3436,plain,
    c_less @ c_0 @ c_1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(766,axiom,
    ! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(2706,plain,
    ! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
      | ( c_in @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
      | ( c_in @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1085,axiom,
    class_Power_Orecpower @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(3304,plain,
    class_Power_Orecpower @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(137,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(1464,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(1026,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(3208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).

thf(1865,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

thf(1635,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(2935,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

thf(1733,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(1109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
      | ( A
        = ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(3340,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
      | ( A
        = ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

thf(1997,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(644,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

thf(2457,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

thf(1897,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(628,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
      | ( c_less @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(2425,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
      | ( c_less @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(1154,axiom,
    class_Divides_Odiv @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(3416,plain,
    class_Divides_Odiv @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(574,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(2319,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(81,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(1356,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(700,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

thf(2573,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

thf(2148,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(1194,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(674,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(2521,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(2119,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

thf(1408,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(970,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

thf(3106,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).

thf(1771,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

thf(1801,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(950,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(3066,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

thf(2065,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(451,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).

thf(2079,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(570,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

thf(2311,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

thf(1282,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(1054,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(3251,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

thf(2642,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(527,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

thf(2229,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(1044,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(3238,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(606,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Sum__Type_OInl @ A @ B @ C )
     != ( c_Sum__Type_OInr @ D @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(2383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Sum__Type_OInl @ A @ B @ C )
     != ( c_Sum__Type_OInr @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(725,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

thf(2624,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

thf(2493,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

thf(2987,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(801,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

thf(2774,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(1073,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(3287,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

thf(1524,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(1349,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).

thf(2097,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

thf(2284,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

thf(2257,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(202,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

thf(1589,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

thf(2955,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(1492,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(564,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

thf(2299,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(270,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

thf(1722,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

thf(2669,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(845,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
      | ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(2856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
      | ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(987,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

thf(3138,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).

thf(1571,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).

thf(1376,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

thf(1439,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(395,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(1969,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(998,axiom,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(3160,plain,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).

thf(1307,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

thf(2111,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

thf(1731,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(364,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

thf(1909,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(1001,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

thf(3165,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(1016,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(3192,plain,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(854,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

thf(2874,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(74,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(1344,plain,
    class_HOL_Ominus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

thf(1460,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(553,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).

thf(2278,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( c_append @ A @ c_List_Olist_ONil @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ( c_append @ A @ c_List_Olist_ONil @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(646,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

thf(2461,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(993,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(3150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(241,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

thf(1667,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(502,axiom,
    class_LOrder_Omeet__semilorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(2180,plain,
    class_LOrder_Omeet__semilorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

thf(2025,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(822,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(2812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(729,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
      | ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(2632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
      | ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

thf(1339,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(716,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

thf(2605,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

thf(2610,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(932,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

thf(3027,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(984,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(3133,plain,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(944,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(3055,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

thf(1557,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

thf(2129,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(586,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).

thf(2343,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

thf(1630,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

thf(1993,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(2410,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(879,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(2923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(329,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

thf(1838,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).

thf(1325,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(807,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

thf(2785,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(710,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

thf(2593,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

thf(2911,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).

thf(1820,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(142,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

thf(1474,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(2171,plain,
    ! [A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

thf(3110,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

thf(1643,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(482,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

thf(2139,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).

thf(2207,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(759,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(2693,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

thf(2069,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

thf(2770,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

thf(2075,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(624,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(2418,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

thf(1396,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(635,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

thf(2439,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(776,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
      | ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
      | ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(2725,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
      | ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
      | ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Olordered__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

thf(1699,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Olordered__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

thf(1528,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(723,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).

thf(2620,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(883,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

thf(2931,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(558,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).

thf(2288,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(1047,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(3241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(927,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

thf(3016,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).

thf(1775,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(790,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

thf(2752,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).

thf(1435,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(1099,axiom,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(3325,plain,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(989,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

thf(3142,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(681,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).

thf(2535,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

thf(2101,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(272,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

thf(1726,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

thf(1364,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(901,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).

thf(2967,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

thf(1496,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(2303,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(918,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(2999,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(1113,axiom,
    ! [A: $i] :
      ( c_0
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(3348,plain,
    ! [A: $i] :
      ( c_0
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

thf(1973,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

thf(1805,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(1130,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(3380,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(1562,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(532,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).

thf(2239,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

thf(2107,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
     != ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(1208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
     != ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).

thf(2665,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

thf(1467,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(991,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

thf(3146,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(881,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

thf(2927,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

thf(1472,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).

thf(1551,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).

thf(2005,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

thf(1413,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

thf(1626,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(923,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(3009,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

thf(2054,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(384,axiom,
    class_Power_Orecpower @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(1948,plain,
    class_Power_Orecpower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

thf(3031,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(824,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2816,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(199,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).

thf(1583,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).

thf(1809,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

thf(2952,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(720,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

thf(2614,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(460,axiom,
    ! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(2096,plain,
    ! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(54,axiom,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(1304,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(346,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(1873,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(1017,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(3193,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(1161,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(3427,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(1141,axiom,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(3395,plain,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(1025,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(3206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).

thf(2471,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(739,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).

thf(2652,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(1077,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(3293,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(999,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).

thf(3161,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).

thf(1905,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(856,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

thf(2878,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(665,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(2503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(251,axiom,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(1684,plain,
    ! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(640,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(2449,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(1509,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(755,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

thf(2684,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(514,axiom,
    ! [B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_List_Oset @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(2202,plain,
    ! [B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_List_Oset @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(1068,axiom,
    ! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(3278,plain,
    ! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(712,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

thf(2597,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(1076,axiom,
    class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

thf(3292,plain,
    class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(867,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

thf(2899,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Olorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).

thf(2942,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

thf(2513,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

thf(1547,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(563,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(2298,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(1128,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(3376,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(2715,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(1961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).

thf(2397,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(973,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

thf(3112,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

thf(1566,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

thf(1647,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ c_List_Olist_ONil @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ c_List_Olist_ONil @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(982,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

thf(3129,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

thf(2821,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(773,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(2720,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_nat )
      | ~ ( c_Divides_Oop_Advd @ A @ C @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

thf(1531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_nat )
      | ~ ( c_Divides_Oop_Advd @ A @ C @ tc_nat )
      | ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

thf(2888,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(858,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

thf(2882,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(832,axiom,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

thf(2831,plain,
    ! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(1092,axiom,
    class_HOL_Otimes @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(3315,plain,
    class_HOL_Otimes @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(906,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(2977,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(602,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).

thf(2375,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != A )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(1225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != A )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

thf(2060,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

thf(1743,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(104,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(1400,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(958,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

thf(3082,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

thf(2192,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
      | ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
      | ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(1037,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(3228,plain,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).

thf(1753,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(946,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

thf(3058,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

thf(2386,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(842,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(2850,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

thf(1484,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(1051,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(3246,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

thf(2092,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

thf(1716,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1111,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(3344,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

thf(1785,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

thf(2429,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

thf(2337,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

thf(1901,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(1152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(3412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).

thf(1579,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(741,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

thf(2656,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(957,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

thf(3080,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(787,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).

thf(2747,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(1086,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(3305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

thf(2165,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).

thf(1300,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).

thf(1452,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

thf(1637,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(974,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).

thf(3114,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(757,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(2688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(1106,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(3334,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(10,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(1188,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

thf(2700,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(1022,axiom,
    class_Numeral_Onumber__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

thf(3202,plain,
    class_Numeral_Onumber__ring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(344,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(1869,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

thf(2276,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(522,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(2219,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

thf(1317,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

thf(1830,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

thf(1763,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(981,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

thf(3127,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(869,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).

thf(2903,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(686,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(2545,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Olorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ( c_List_Oset @ c_List_Olist_ONil @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(2599,plain,
    ! [A: $i] :
      ( ( c_List_Oset @ c_List_Olist_ONil @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(1117,axiom,
    class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(3359,plain,
    class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

thf(2044,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

thf(1543,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(401,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(1981,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).

thf(2379,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(685,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

thf(2543,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(769,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

thf(2711,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(703,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

thf(2579,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(1136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
      | ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(3388,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
      | ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(887,axiom,
    class_LOrder_Ojoin__semilorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(2939,plain,
    class_LOrder_Ojoin__semilorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(1143,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(3398,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1074,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(3288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(1240,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(751,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

thf(2675,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

thf(2056,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(536,axiom,
    class_Parity_Oeven__odd @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(2247,plain,
    class_Parity_Oeven__odd @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

thf(1934,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(892,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

thf(2948,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(836,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(2838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

thf(2113,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(1153,axiom,
    class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

thf(3415,plain,
    class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

thf(1284,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(905,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

thf(2975,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

thf(1353,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(2357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).

thf(1955,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

thf(2843,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

thf(1749,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(1034,axiom,
    class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

thf(3224,plain,
    class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).

thf(1427,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(200,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

thf(1585,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(669,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

thf(2511,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).

thf(1670,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

thf(1797,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(976,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

thf(3117,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

thf(2860,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

thf(2722,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(90,axiom,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(1372,plain,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(863,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(2892,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

thf(1881,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(819,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).

thf(2807,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(996,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).

thf(3156,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(841,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

thf(2848,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(1122,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(3366,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(922,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

thf(3007,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

thf(2266,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(380,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(1940,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

thf(2760,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__ring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(1165,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(3433,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(655,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_IntDef_Oint @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(2479,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_IntDef_Oint @ A )
       != ( c_IntDef_Oint @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).

thf(3092,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(1685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

thf(1844,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).

thf(2325,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

thf(3056,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(938,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Sum__Type_OInl @ A @ B @ C )
       != ( c_Sum__Type_OInl @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(3039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Sum__Type_OInl @ A @ B @ C )
       != ( c_Sum__Type_OInl @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

thf(1421,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(2013,plain,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

thf(2626,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(232,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

thf(1649,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(1145,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(3401,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

thf(2088,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

thf(2696,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

thf(1553,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(1949,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(852,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

thf(2870,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(1004,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

thf(3171,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(899,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype_Ooption_OSome @ A @ B )
       != ( c_Datatype_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(2960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype_Ooption_OSome @ A @ B )
       != ( c_Datatype_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).

thf(1834,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).

thf(1913,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(1013,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
      | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(3188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
      | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).

thf(2194,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(588,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).

thf(2347,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(110,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(1412,plain,
    class_Ring__and__Field_Osemiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

thf(2215,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

thf(1517,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

thf(1781,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(1216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).

thf(2209,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(785,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

thf(2743,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).

thf(1448,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(2187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(1390,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(567,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(2305,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(877,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(2919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).

thf(1575,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(2071,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

thf(2658,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(811,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

thf(2792,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).

thf(1807,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(871,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

thf(2907,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

thf(2591,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).

thf(2443,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(767,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

thf(2707,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

thf(2167,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(72,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(1341,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(691,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(2554,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(1133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(3383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(821,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(2811,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

thf(1745,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

thf(2971,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(1854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

thf(2431,plain,
    ! [A: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(1055,axiom,
    class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(3252,plain,
    class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(623,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(2416,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

thf(2174,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).

thf(2389,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

thf(1476,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(245,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).

thf(1674,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).

thf(1639,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(2290,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).

thf(2251,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).

thf(1903,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(480,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).

thf(2135,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(618,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

thf(2406,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(1124,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(3369,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

thf(2823,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(1032,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(3220,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).

thf(3003,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(1244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(796,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).

thf(2764,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).

thf(1822,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(1104,axiom,
    class_LOrder_Olorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(3331,plain,
    class_LOrder_Olorder @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(986,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

thf(3136,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Sum__Type_OInr @ A @ B @ C )
     != ( c_Sum__Type_OInl @ D @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(2152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Sum__Type_OInr @ A @ B @ C )
     != ( c_Sum__Type_OInl @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(2262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(1098,axiom,
    class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

thf(3324,plain,
    class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(813,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

thf(2796,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(614,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(2399,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

thf(1294,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

thf(2330,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

thf(2198,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(262,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

thf(1706,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(595,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(2362,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

thf(2183,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

thf(1661,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

thf(2315,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(876,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

thf(2917,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

thf(2447,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(890,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(2944,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(416,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

thf(2009,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(340,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(1861,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(254,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

thf(1689,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

thf(2081,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(1009,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).

thf(3181,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

thf(2475,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).

thf(2648,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(1163,axiom,
    class_Parity_Oeven__odd @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(3430,plain,
    class_Parity_Oeven__odd @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Oone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).

thf(1777,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Oone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(1114,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(3351,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
       != c_0 )
      | ( A
        = ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(1513,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

thf(2036,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(57,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(1309,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(356,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

thf(1893,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).

thf(2294,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(2739,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

thf(1444,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(2779,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ominus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).

thf(2019,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_HOL_Ominus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(1157,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(3420,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(214,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).

thf(1614,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

thf(2421,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(2123,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(672,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).

thf(2517,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(1280,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

thf(1957,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

thf(1678,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(910,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

thf(2983,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(707,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(2587,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

thf(2233,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(967,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

thf(3100,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

thf(1986,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(1107,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(3337,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).

thf(2050,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(288,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(1757,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).

thf(2003,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(484,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).

thf(2142,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(1129,axiom,
    class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

thf(3379,plain,
    class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).

thf(2155,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(541,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

thf(2255,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(1593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

thf(1380,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).

thf(2768,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

thf(1480,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1023,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(3203,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(948,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(3062,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(1859,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(1102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(3328,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

thf(1989,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(1314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(318,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

thf(1816,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(1007,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).

thf(3177,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).

thf(1789,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

thf(2366,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1159,axiom,
    class_Ring__and__Field_Oring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

thf(3424,plain,
    class_Ring__and__Field_Oring @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(432,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
      | ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(2040,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
      | ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(940,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

thf(3045,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(806,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(2783,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(688,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(2549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(1088,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(3309,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(731,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).

thf(2636,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(1657,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(581,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(2334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).

thf(1335,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).

thf(1693,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(187,axiom,
    ! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(1561,plain,
    ! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

thf(2704,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
      | ( class_HOL_Otimes @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(3,axiom,
    c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(1172,plain,
    c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(1410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).

thf(1288,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Osemiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

thf(1710,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).

thf(2913,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Oring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(617,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

thf(2404,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(1097,axiom,
    class_HOL_Ominus @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(3323,plain,
    class_HOL_Ominus @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(1019,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(3196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(355,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(1891,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_LOrder_Ojoin__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).

thf(2021,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

thf(1610,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(591,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

thf(2353,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
      | ( class_OrderedGroup_Olordered__ab__group @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(1049,axiom,
    class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).

thf(3244,plain,
    class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

thf(1977,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(931,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

thf(3025,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(38,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( A
        = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(1268,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
      | ( A
        = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(649,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(2467,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

thf(2507,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(1138,axiom,
    class_HOL_Oplus @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(3392,plain,
    class_HOL_Oplus @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).

thf(1925,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(2539,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

thf(1885,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(600,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(2372,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
       != ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(1236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
       != ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).

thf(2241,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

thf(2127,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(492,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

thf(2159,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(779,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).

thf(2731,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(817,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).

thf(2803,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(840,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(2847,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

thf(1384,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
      | ( class_LOrder_Omeet__semilorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).

thf(2485,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).

thf(1537,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(1118,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(3360,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Ozero @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(1378,plain,
    ! [A: $i] :
      ( ~ ( class_Power_Orecpower @ A )
      | ( class_HOL_Ozero @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

thf(1357,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(705,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

thf(2583,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(1060,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
      | ( A
        = ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(3259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
      | ( A
        = ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(155,axiom,
    ! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1500,plain,
    ! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).

thf(1923,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(1050,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(3245,plain,
    class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(929,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

thf(3020,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(849,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

thf(2864,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(1431,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(955,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

thf(3076,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(1140,axiom,
    class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).

thf(3394,plain,
    class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

thf(1505,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).

thf(2270,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ( class_Ring__and__Field_Osemiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

thf(2754,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(733,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).

thf(2640,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(1168,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(3437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).

thf(2563,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(1082,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(3299,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(1148,axiom,
    class_Numeral_Onumber @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(3405,plain,
    class_Numeral_Onumber @ tc_IntDef_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(917,axiom,
    ! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(2998,plain,
    ! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(633,axiom,
    ! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(2436,plain,
    ! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(334,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

thf(1848,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).

thf(1490,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(642,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

thf(2453,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_Ring__and__Field_Osemiring__1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(455,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(2087,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(941,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

thf(3047,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(1080,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(3296,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

thf(1417,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

thf(1331,plain,
    ! [A: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ A )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

thf(1606,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(575,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

thf(2321,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

thf(1653,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

thf(1944,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

thf(3096,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(1737,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).

thf(2866,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

thf(2832,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

thf(1769,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(368,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

thf(1917,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
      | ( class_HOL_Oplus @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(1093,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(3316,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).

thf(2834,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(590,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

thf(2351,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( class_OrderedGroup_Osemigroup__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(915,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ A @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(2993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ A @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(1021,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(3200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(508,axiom,
    class_Orderings_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(2191,plain,
    class_Orderings_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(1204,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)],[15]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

thf(1812,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(908,axiom,
    class_Divides_Odiv @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(2980,plain,
    class_Divides_Odiv @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

thf(3035,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(3439,plain,
    $false,
    inference(e,[status(thm)],[2163,1665,2630,1501,2094,1767,1559,3167,2921,1840,1179,1818,1549,2280,2250,1879,1337,1718,2612,1469,3053,3345,2341,2336,2109,2131,1454,2031,3399,1995,2412,2876,2463,1899,2787,2595,1850,2499,2427,1982,2077,3185,1211,2309,3072,1290,2527,1401,3098,2671,3012,1305,1437,3382,2117,2940,1596,2231,2622,1522,2644,2495,3230,2381,2395,2062,2776,3417,1618,3285,1569,2248,1728,3108,2099,2282,1591,1971,1793,3402,2854,1533,1173,1486,1608,1655,3049,1310,3365,1735,1999,1327,2901,2042,2146,1458,1426,3217,2607,2686,3332,3367,1867,3175,3338,2933,1275,2141,1919,3253,1988,2459,1761,1342,3121,1507,1222,2360,3276,2575,3370,3236,2046,1441,3088,1366,2531,1887,2957,2985,2227,1645,1921,2886,1359,1386,3281,3140,1724,2400,1967,2067,2825,2819,1803,1228,1482,1254,3204,2603,3425,2339,1871,2217,2654,1628,3195,3029,2735,2814,2698,3131,1298,3116,2667,1907,2501,1323,3148,1511,2274,2682,3125,1826,3410,2185,1577,1832,2897,1191,1462,3043,2745,2571,1545,2691,2713,2169,3216,2929,3014,1641,1773,1875,3268,2829,3374,3385,1247,2552,1319,1704,2373,1347,1741,1398,3084,3312,1931,1568,2301,1494,2989,1362,1963,2852,3231,2388,2533,2007,3322,3431,2996,2259,2451,3357,1581,2017,2178,2222,2950,2237,1415,2616,1946,1465,1302,2794,1714,2027,2105,1811,1450,2090,3393,1911,3295,2893,1632,2469,3163,2650,2880,1682,1828,2925,1677,2034,3290,3300,2777,3152,1183,2073,2964,2058,1169,2437,3068,2618,3421,2483,2523,1622,1351,1600,2884,2762,1394,2772,1526,2137,3361,3243,2809,1345,2799,2286,3327,1433,2103,2750,1405,3226,1201,1697,1242,3211,1521,3406,2205,1975,1564,1604,2011,3229,3011,3303,2473,1691,2364,3318,3418,1863,3435,2954,1651,3169,3265,2646,1915,1708,1783,2737,2296,2307,2083,2790,2660,2905,1730,3037,2589,2264,2601,2541,1519,1355,2969,3239,2015,1883,2441,2673,2733,2560,2805,1676,2133,3022,1751,3233,2937,3154,3134,1824,2150,1370,2890,2414,3250,1602,2628,3297,1296,1687,1624,2200,3144,2345,2211,2741,1573,3282,2958,1423,3307,3271,2445,3191,1938,2758,2433,2477,3090,2565,3198,2663,1555,2332,3314,2872,1951,1836,1787,2181,2327,2213,2547,2313,1634,1392,3033,3408,3105,1953,2895,2841,2973,2709,2694,1878,3119,3078,1755,2638,2268,3001,2245,1936,1234,1541,2157,2115,2515,3254,1259,2946,2377,2801,2577,3381,1498,1587,2509,3102,1672,2724,2858,2537,3060,3018,2798,3311,1361,1292,1182,2868,2419,1889,2023,3326,1942,1659,2323,3179,2561,3210,3094,1739,1424,2455,2196,1842,1791,3428,1214,2349,2038,1446,2551,2085,1612,2978,2317,3294,2781,1419,2125,2681,2243,1984,1852,2756,1759,2370,1478,1249,2519,1530,1539,2836,1456,1382,2487,2845,1266,3354,1231,2355,1932,2581,2465,2505,3390,3222,2497,2566,1799,1429,3247,2862,2766,2052,3064,1720,1979,3074,3005,2272,3364,1333,1991,2702,1779,1695,3173,1170,2402,2915,1515,1895,2909,2634,2749,1857,1814,3225,3279,3183,1712,1846,1286,2368,2408,1663,3190,2189,1616,2662,1185,2423,2529,1278,2729,2001,2292,2585,1927,3262,3274,1374,3396,2121,2235,2144,2677,2176,2391,1680,1959,2556,2253,2033,3257,2717,1219,2570,1747,3343,3158,2260,3372,3319,2225,3255,3240,2789,2525,2981,1929,1403,1965,2827,3213,3387,3187,3070,2727,3234,2048,1620,2489,2393,3086,1388,3272,1535,2991,1795,1701,3404,2817,1256,1488,2161,1503,1669,2220,2029,1271,1312,3330,3123,3436,2706,1765,3304,1464,3208,1865,1635,2935,1733,3340,1997,2457,1897,2425,3416,2319,1356,2573,2148,1194,2521,2119,1408,3106,1771,1801,3066,2065,2079,2311,1282,3251,2642,2229,3238,2383,2624,2493,2987,2774,3287,1524,1349,2097,2284,2257,1589,2955,1492,2299,1722,2669,2856,3138,1571,1376,1439,1969,3160,1307,2111,1731,1909,3165,3192,2874,1344,1460,2278,1177,2461,3150,1667,2180,2025,2812,2632,1339,2605,2610,3027,3133,3055,1557,2129,2343,1630,1993,2410,2923,1838,1325,2785,2593,2911,1820,1474,2171,3110,1643,2139,2207,2693,2069,2770,2075,2418,1396,2439,2725,1699,1528,2620,2931,2288,3241,3016,1775,2752,1435,3325,3142,2535,2101,1726,1364,2967,1496,2303,2999,3348,1973,1805,3380,1562,2239,2107,1208,2665,1467,3146,2927,1472,1551,2005,1413,1626,3009,2054,1948,3031,2816,1583,1809,2952,2614,2096,1304,1873,3193,3427,3395,3206,2471,2652,3293,3161,1905,2878,2503,1684,2449,1509,2684,2202,3278,2597,3292,2899,2942,2513,1547,2298,3376,2715,1961,2397,3112,1566,1647,1252,3129,2821,2720,1531,2888,2882,2831,3315,1598,2977,2375,1225,2060,1743,1400,3082,2192,1368,3228,1753,3058,2386,2850,1484,3246,2092,1716,3344,1785,2429,1262,2337,1901,3412,1579,2656,3080,2747,3305,2165,1300,1452,1637,3114,2688,3334,1188,2700,3202,1869,2276,2219,1317,1830,1763,3127,2903,2545,2599,3359,2044,1543,1981,2379,2543,2711,2579,3388,2939,3398,3288,1240,2675,2056,2247,1934,2948,2838,2113,3415,1284,2975,1353,2357,1955,2843,1749,3224,1427,1585,2511,1670,1797,3117,2860,2722,1372,2892,1881,2807,3156,2848,3366,3007,2266,1940,2760,3433,2479,3092,1685,1844,2325,3056,3039,1421,2013,2626,1649,3401,2088,2696,1553,1949,2870,3171,2960,1321,1834,1913,3188,2194,2347,1412,2215,1517,1781,1216,2209,2743,1448,2187,1390,2305,2919,1575,2071,2658,2792,1807,2907,2591,2443,2707,2167,1341,2554,3383,2811,1745,2971,1854,2431,3252,2416,2174,2389,1476,1674,1639,2290,2251,1903,2135,2406,3369,2823,3220,3003,1244,2764,1822,3331,3136,2152,2262,3324,2796,2399,1294,2330,2198,1706,2362,2183,1661,2315,2917,2447,2944,2009,1861,1689,2081,3181,2475,2648,3430,1777,3351,1513,2036,1309,1893,2294,2739,1444,2779,2019,3420,1614,2421,2123,2517,1280,1957,1678,2983,2587,2233,3100,1986,3337,2050,1757,2003,2142,3379,2155,2255,1593,1380,2768,1480,3203,3062,1859,3328,1989,1314,1816,3177,1789,2366,3424,2040,3045,2783,2549,3309,2636,1657,2334,1335,1693,1561,2704,1172,1410,1288,1710,1197,2913,2404,3323,3196,1891,2021,1610,2353,3244,1977,3025,1268,2467,2507,3392,1925,2539,1885,2372,1236,2241,2127,2159,2731,2803,2847,1384,2485,1537,3360,1378,1357,2583,3259,1500,1923,3245,3020,2864,1431,3076,3394,1505,2270,2754,2640,3437,2563,3299,3405,2998,2436,1848,1490,2453,2087,3047,3296,1417,1331,1606,2321,1653,1944,3096,1737,2866,2832,1769,1917,3316,2834,2351,2993,3200,2191,1204,1812,2980,3035]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET818-1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n027.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 19:21:21 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.90/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.69/1.06  % [INFO] 	 Parsing done (239ms). 
% 1.69/1.07  % [INFO] 	 Running in sequential loop mode. 
% 2.33/1.27  % [INFO] 	 eprover registered as external prover. 
% 2.33/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 2.33/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.80/1.38  % [INFO] 	 Found a conjecture and 1357 axioms. Running axiom selection ... 
% 3.41/1.58  % [INFO] 	 Axiom selection finished. Selected 1166 axioms (removed 191 axioms). 
% 3.94/1.72  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.94/1.73  % [INFO] 	 Type checking passed. 
% 3.94/1.74  % [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 ... 
% 10.34/3.38  % External prover 'e' found a proof!
% 10.34/3.39  % [INFO] 	 Killing All external provers ... 
% 10.34/3.39  % Time passed: 2884ms (effective reasoning time: 2310ms)
% 10.34/3.39  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.34/3.39  % Axioms used in derivation (1166): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Oidom_20, clsrel_Ring__and__Field_Oordered__idom_3, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Oidom_17, clsarity_IntDef__Oint_57, clsrel_OrderedGroup_Olordered__ab__group__abs_3, clsrel_Ring__and__Field_Osemiring__1__cancel_12, cls_Nat_Ole__0__eq__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, clsrel_Ring__and__Field_Opordered__comm__semiring_14, clsrel_Ring__and__Field_Opordered__ring_2, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, clsrel_Ring__and__Field_Oring__1_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, cls_IntDiv_Ozdvd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, clsarity_IntDef__Oint_4, cls_List_Ofinite__set_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, clsrel_Ring__and__Field_Ocomm__ring_3, clsrel_Ring__and__Field_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodI_0, clsrel_Ring__and__Field_Oordered__semidom_16, clsrel_OrderedGroup_Opordered__ab__group__add_6, clsarity_nat_32, clsarity_nat_26, clsrel_Numeral_Onumber__ring_1, clsrel_Ring__and__Field_Olordered__ring_8, clsrel_Ring__and__Field_Ocomm__ring_12, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Oordered__ring__strict_7, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, clsrel_Ring__and__Field_Olordered__ring_14, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsrel_Ring__and__Field_Ocomm__ring_17, cls_List_Olists_ONil_0, cls_Set_OInterD_0, clsarity_IntDef__Oint_45, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20, clsrel_Power_Orecpower_17, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7, clsrel_OrderedGroup_Olordered__ab__group_13, cls_Divides_Omod__eq__0D__dest_0, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_6, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Ring__and__Field_Oordered__idom_43, clsrel_OrderedGroup_Olordered__ab__group_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_7, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oring_13, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, clsrel_OrderedGroup_Omonoid__mult_2, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_SetInterval_OgreaterThan__iff__iff2_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, clsrel_Ring__and__Field_Oordered__idom_12, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, clsarity_nat_15, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4, cls_List_ONil__is__append__conv__iff2_0, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_10, clsrel_Ring__and__Field_Olordered__ring_3, clsrel_Power_Orecpower_14, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_Ring__and__Field_Oidom_29, clsarity_IntDef__Oint_24, clsrel_Ring__and__Field_Oidom_26, clsrel_OrderedGroup_Osemigroup__add_0, clsrel_Ring__and__Field_Oring_10, clsrel_Numeral_Onumber__ring_16, clsrel_OrderedGroup_Olordered__ab__group_9, clsrel_Power_Orecpower_6, clsarity_nat_10, clsrel_Ring__and__Field_Oordered__ring__strict_26, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_Ring__and__Field_Oidom_13, clsrel_Ring__and__Field_Opordered__ring_14, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__ring__1_1, clsrel_Ring__and__Field_Oring__1_18, clsrel_OrderedGroup_Oab__group__add_6, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, clsrel_OrderedGroup_Olordered__ab__group__abs_8, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, clsrel_Ring__and__Field_Ocomm__ring__1_16, cls_Nat_Oless__Suc0__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, clsrel_Numeral_Onumber__ring_27, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, clsrel_Ring__and__Field_Opordered__ring_19, cls_Finite__Set_OFinites_OemptyI_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, clsrel_Numeral_Onumber__ring_24, clsrel_Ring__and__Field_Oordered__semidom_23, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsrel_Power_Orecpower_5, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4, clsrel_OrderedGroup_Olordered__ab__group__abs_13, clsrel_Ring__and__Field_Ocomm__ring__1_20, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, clsrel_Ring__and__Field_Oordered__idom_48, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, clsrel_Ring__and__Field_Olordered__ring_4, clsrel_Ring__and__Field_Osemiring_1, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsrel_Ring__and__Field_Oordered__ring__strict_14, clsrel_Ring__and__Field_Oordered__idom_56, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, cls_Finite__Set_OFinites_OinsertI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, clsrel_Ring__and__Field_Oidom_10, clsarity_set_2, clsarity_nat_25, clsrel_Ring__and__Field_Oordered__idom_17, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Oring_6, clsrel_OrderedGroup_Olordered__ab__group__join_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Ring__and__Field_Oring__1_19, clsrel_OrderedGroup_Oab__group__add_5, clsrel_Ring__and__Field_Olordered__ring_1, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsrel_Ring__and__Field_Oring__1_14, cls_List_Olistrel__Nil1_0, clsrel_Numeral_Onumber__ring_12, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, clsrel_Ring__and__Field_Ocomm__ring__1_5, clsarity_IntDef__Oint_3, cls_Nat_Onot__less0__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, clsrel_Ring__and__Field_Ocomm__ring__1_13, clsrel_OrderedGroup_Olordered__ab__group__meet_9, clsarity_IntDef__Oint_60, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Numeral_Onumber__ring_23, clsrel_Numeral_Onumber__ring_20, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_Nat_Oless__one__iff1_0, clsrel_Ring__and__Field_Ocomm__ring_9, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, clsrel_Ring__and__Field_Oidom_1, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Set_OComplI_0, clsrel_OrderedGroup_Opordered__ab__group__add_8, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_Ring__and__Field_Ocomm__semiring__0_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__comm__semiring_8, clsrel_Ring__and__Field_Ocomm__ring__1_27, cls_Relation_OconverseE_1, clsrel_Ring__and__Field_Olordered__ring_21, clsrel_OrderedGroup_Oab__group__add_0, clsarity_nat_47, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_14, cls_Finite__Set_Ofinite__Int_0, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, clsrel_OrderedGroup_Opordered__ab__group__add_10, clsrel_Ring__and__Field_Oordered__idom_28, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsrel_Ring__and__Field_Oordered__semiring__strict_19, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, clsrel_Ring__and__Field_Osemiring__1_4, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, clsrel_Ring__and__Field_Oidom_21, clsarity_IntDef__Oint_49, clsrel_Ring__and__Field_Ocomm__ring_10, clsrel_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, clsrel_Ring__and__Field_Opordered__ring_6, clsarity_IntDef__Oint_38, clsrel_Ring__and__Field_Oring_1, clsrel_Ring__and__Field_Oidom_7, clsrel_Ring__and__Field_Opordered__ring_11, clsrel_OrderedGroup_Oab__semigroup__mult_0, clsrel_Ring__and__Field_Opordered__semiring_2, clsrel_Ring__and__Field_Opordered__ring_22, clsrel_Ring__and__Field_Osemiring__0_2, clsrel_Ring__and__Field_Ocomm__ring_13, cls_SetInterval_OlessThan__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_49, clsrel_Ring__and__Field_Osemiring__0_7, cls_Set_OUnCI_1, clsrel_OrderedGroup_Olordered__ab__group__meet_12, clsrel_Ring__and__Field_Oring__1_2, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14, clsarity_IntDef__Oint_16, clsrel_Ring__and__Field_Oordered__semiring__strict_3, clsrel_Ring__and__Field_Osemiring__1_10, cls_Relation_ORangeE_0, clsrel_Ring__and__Field_Oordered__semiring__strict_8, cls_Set_OInterI_1, clsrel_Numeral_Onumber__ring_19, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_OrderedGroup_Olordered__ab__group__abs_10, cls_List_Oset__empty__iff2_0, clsrel_Numeral_Onumber__ring_5, clsrel_Ring__and__Field_Ocomm__semiring__1_16, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, clsarity_nat_36, clsrel_Ring__and__Field_Olordered__ring_25, clsrel_Ring__and__Field_Ocomm__ring_0, clsarity_nat_18, clsrel_Ring__and__Field_Oordered__semidom_13, cls_Product__Type_OPair__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_Set_OinsertCI_0, clsrel_Ring__and__Field_Olordered__ring_10, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, cls_Set_OPow__iff__iff2_0, clsrel_Ring__and__Field_Oring__1_11, cls_Finite__Set_Ofinite__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Opordered__ab__group__add_11, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Power_Orecpower_13, clsrel_Ring__and__Field_Oordered__semidom_24, clsarity_IntDef__Oint_19, clsrel_Ring__and__Field_Oordered__semiring__strict_16, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5, clsrel_OrderedGroup_Olordered__ab__group_4, cls_List_Oappend__in__lists__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semiring__strict_21, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, clsrel_Ring__and__Field_Oring__1_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, clsrel_Ring__and__Field_Oidom_25, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Oordered__ring__strict_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsarity_IntDef__Oint_59, clsarity_nat_22, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, clsrel_OrderedGroup_Ocomm__monoid__mult_3, cls_Set_OCompl__subset__Compl__iff__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29, cls_Datatype__Universe_OIn0__not__In1__iff1_0, clsrel_Power_Orecpower_18, clsrel_Ring__and__Field_Oidom_6, clsrel_Ring__and__Field_Opordered__ring_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, clsarity_nat_44, clsrel_OrderedGroup_Olordered__ab__group__abs_4, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, clsrel_Ring__and__Field_Osemiring__1__cancel_4, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Oring__1_6, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Osemiring__1_3, cls_Finite__Set_Ofinite__Un__iff1_0, clsrel_Numeral_Onumber__ring_6, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Datatype__Universe_OdprodE_1, clsrel_OrderedGroup_Olordered__ab__group_6, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, cls_Set_OUNIV__I_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, clsrel_Ring__and__Field_Ocomm__semiring_2, clsrel_Numeral_Onumber__ring_28, clsarity_IntDef__Oint_58, cls_Set_OCompl__eq__Compl__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, clsrel_Ring__and__Field_Oordered__idom_38, clsrel_Ring__and__Field_Oordered__idom_2, clsrel_OrderedGroup_Olordered__ab__group__abs_5, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__semidom_3, clsrel_Ring__and__Field_Opordered__ring_3, cls_List_OlistsE_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5, cls_List_Olength__0__conv__iff2_0, clsrel_Power_Orecpower_4, cls_Divides_Odvd__0__left__iff__iff2_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0, cls_List_Oself__append__conv__iff2_0, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Olordered__ring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_11, clsarity_IntDef__Oint_53, cls_List_Owf__lex_0, cls_SetInterval_OatMost__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_36, clsarity_nat_27, cls_Relation_ODomainI_0, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, clsrel_Ring__and__Field_Ocomm__semiring_5, clsrel_Ring__and__Field_Oordered__idom_26, cls_Set_OinsertE_0, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_Ring__and__Field_Oring__1_15, clsrel_Ring__and__Field_Oordered__ring__strict_8, clsrel_Ring__and__Field_Oordered__idom_52, clsrel_Ring__and__Field_Oordered__ring__strict_25, clsrel_Ring__and__Field_Opordered__semiring_7, clsrel_Ring__and__Field_Ocomm__ring__1_0, clsarity_IntDef__Oint_64, clsrel_Ring__and__Field_Opordered__ring_13, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, clsrel_OrderedGroup_Ocomm__monoid__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_27, cls_Set_Onot__psubset__empty__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_14, clsarity_IntDef__Oint_14, clsrel_Ring__and__Field_Opordered__comm__semiring_13, clsarity_IntDef__Oint_7, cls_Set_OUnE_0, clsrel_Ring__and__Field_Oring_9, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring__1_10, clsrel_OrderedGroup_Olordered__ab__group_0, clsarity_nat_16, clsrel_Ring__and__Field_Opordered__cancel__semiring_12, cls_SetInterval_OlessThan__subset__iff__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, clsrel_OrderedGroup_Olordered__ab__group_14, clsrel_Ring__and__Field_Oidom_14, clsrel_Ring__and__Field_Ocomm__semiring__1_11, clsrel_Ring__and__Field_Oordered__idom_10, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_Ring__and__Field_Oordered__ring__strict_36, clsrel_Ring__and__Field_Osemiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__ring__strict_11, clsrel_Ring__and__Field_Ocomm__ring_16, clsrel_Ring__and__Field_Olordered__ring_19, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, clsrel_Ring__and__Field_Ocomm__ring__1_21, clsrel_Ring__and__Field_Oordered__idom_47, clsrel_Ring__and__Field_Ocomm__ring_2, clsarity_nat_38, clsrel_Ring__and__Field_Oordered__ring__strict_5, clsrel_Numeral_Onumber__ring_2, clsrel_Numeral_Onumber__ring_17, cls_Set_OComplD__dest_0, clsrel_Ring__and__Field_Ocomm__semiring__0_3, clsrel_Ring__and__Field_Oordered__semidom_8, cls_Set_OUn__empty__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12, cls_Relation_Orel__compE_2, clsrel_Ring__and__Field_Oordered__idom_15, clsrel_Ring__and__Field_Ocomm__ring__1_19, clsrel_OrderedGroup_Olordered__ab__group_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, cls_Relation_OImageE_1, cls_Set_OsingletonD__dest_0, clsrel_Ring__and__Field_Olordered__ring_7, clsarity_IntDef__Oint_20, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Ocomm__ring__1_4, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_16, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, clsrel_Ring__and__Field_Ocomm__ring__1_14, clsrel_Ring__and__Field_Oordered__idom_31, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OdiagE_0, clsrel_Ring__and__Field_Ocomm__ring__1_26, cls_SetInterval_Ofinite__atLeastAtMost_0, clsrel_Ring__and__Field_Oordered__ring__strict_21, cls_SetInterval_OatMost__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, cls_GCD_Ogcd__dvd1_0, clsrel_Ring__and__Field_Oring_5, cls_SetInterval_Ofinite__atLeastLessThan_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Olordered__ab__group__join_7, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, clsrel_Ring__and__Field_Olordered__ring_26, cls_Set_OUn__empty__iff1_0, clsrel_Ring__and__Field_Oordered__idom_22, clsrel_Power_Orecpower_10, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, clsrel_Ring__and__Field_Oordered__idom_57, clsrel_Ring__and__Field_Opordered__cancel__semiring_2, cls_Wellfounded__Recursion_Owf__insert__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_4, clsrel_Ring__and__Field_Opordered__ring_12, clsrel_Ring__and__Field_Osemiring__0_6, clsrel_Ring__and__Field_Oordered__ring__strict_4, cls_Set_Oempty__subsetI_0, clsrel_Numeral_Onumber__ring_13, clsrel_Ring__and__Field_Ocomm__ring__1_25, clsrel_OrderedGroup_Olordered__ab__group__join_13, clsrel_Ring__and__Field_Oordered__ring__strict_32, cls_Relation_OIdI_0, clsarity_IntDef__Oint_26, clsrel_Ring__and__Field_Ocomm__ring__1_15, clsarity_IntDef__Oint_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15, cls_List_Oappend__is__Nil__conv__iff2_0, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_11, clsrel_Ring__and__Field_Oordered__semidom_17, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, clsrel_Ring__and__Field_Oordered__idom_29, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, clsrel_Ring__and__Field_Oordered__ring__strict_15, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_Ring__and__Field_Osemiring__1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_14, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_11, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2, cls_Nat_Oadd__gr__0__iff2_1, clsrel_Ring__and__Field_Opordered__ring_9, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_2, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_8, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, clsrel_Ring__and__Field_Oring_2, cls_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__idom_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, clsrel_Ring__and__Field_Olordered__ring_22, clsarity_nat_37, cls_Product__Type_OPair__eq__iff1_1, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, clsrel_Ring__and__Field_Oaxclass__abs__if_1, clsrel_Ring__and__Field_Oidom_11, clsrel_Ring__and__Field_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, cls_List_Osame__append__eq__iff1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Oidom_2, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, clsrel_Ring__and__Field_Oring__1_1, cls_SetInterval_OatLeast__iff__iff2_0, cls_GCD_Ogcd__greatest__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, clsrel_OrderedGroup_Opordered__ab__group__add_2, cls_Datatype_Oelem__o2s__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__meet_11, clsrel_Ring__and__Field_Olordered__ring_11, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__0_10, clsrel_Ring__and__Field_Opordered__ring_7, cls_Relation_OconverseE_0, clsarity_IntDef__Oint_42, clsrel_OrderedGroup_Oab__group__add_4, cls_IntDiv_Ozdvd__1__left_0, cls_List_Olength__greater__0__conv__iff2_0, clsrel_Numeral_Onumber__ring_30, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__idom_39, cls_SetInterval_OatMost__subset__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_6, clsrel_Ring__and__Field_Opordered__comm__semiring_9, clsrel_Ring__and__Field_Oordered__semidom_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0, cls_GCD_Ogcd__greatest__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_11, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6, clsarity_nat_0, cls_Datatype__Universe_OuprodE_2, clsarity_nat_43, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_0, clsrel_Ring__and__Field_Osemiring__1_7, cls_Datatype__Universe_OIn1__not__In0__iff1_0, clsarity_IntDef__Oint_18, cls_List_Olist_Oinject__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_13, clsrel_Ring__and__Field_Opordered__cancel__semiring_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, clsrel_Numeral_Onumber__ring_7, clsarity_nat_34, clsrel_Ring__and__Field_Ocomm__semiring__1_10, clsrel_OrderedGroup_Olordered__ab__group_5, clsrel_Ring__and__Field_Opordered__ring_17, clsrel_OrderedGroup_Olordered__ab__group__abs_6, clsrel_OrderedGroup_Opordered__ab__semigroup__add_3, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_8, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8, clsrel_Ring__and__Field_Oordered__semidom_25, clsrel_OrderedGroup_Opordered__ab__group__add_4, clsrel_LOrder_Omeet__semilorder_0, clsrel_Ring__and__Field_Olordered__ring_18, clsrel_Power_Orecpower_3, clsarity_IntDef__Oint_29, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1, clsrel_Ring__and__Field_Osemiring__0_1, cls_GCD_Ogcd__greatest__iff__iff1_1, clsrel_Orderings_Olinorder_2, cls_Datatype__Universe_OuprodE_0, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8, clsrel_Ring__and__Field_Olordered__ring_23, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring_1, clsrel_Ring__and__Field_Oordered__idom_46, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_OrderedGroup_Olordered__ab__group__meet_10, clsrel_Ring__and__Field_Oordered__idom_19, clsarity_nat_45, cls_Set_ODiffE_0, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_Ring__and__Field_Olordered__ring_12, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsarity_nat_17, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, clsrel_Ring__and__Field_Ocomm__ring__1_2, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, clsrel_Ring__and__Field_Oidom_9, cls_Relation_ORangeI_0, cls_Divides_Odvd__triv__right_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__idom_14, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsrel_Ring__and__Field_Oordered__idom_20, clsrel_Ring__and__Field_Opordered__comm__semiring_12, clsrel_Ring__and__Field_Ocomm__ring_1, clsrel_OrderedGroup_Olordered__ab__group__join_11, clsrel_Ring__and__Field_Opordered__cancel__semiring_5, clsrel_Ring__and__Field_Oordered__semidom_27, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, clsrel_Ring__and__Field_Oidom_15, cls_List_Oset__empty__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, clsrel_Ring__and__Field_Oidom_24, clsrel_Ring__and__Field_Oordered__semidom_4, clsrel_Numeral_Onumber__ring_22, cls_Nat_Onot__add__less1__iff1_0, clsrel_Numeral_Onumber__ring_11, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, clsarity_IntDef__Oint_8, clsrel_Ring__and__Field_Opordered__cancel__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16, cls_Relation_Opair__in__Id__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4, clsrel_Ring__and__Field_Opordered__ring_0, clsarity_IntDef__Oint_54, clsarity_nat_28, clsrel_Ring__and__Field_Ocomm__semiring_6, cls_Set_OIntI_0, clsrel_Ring__and__Field_Ocomm__ring_8, clsrel_Ring__and__Field_Osemiring__0__cancel_6, clsarity_nat_39, cls_Finite__Set_Ofinite__Union_1, clsrel_LOrder_Ojoin__semilorder_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, clsrel_OrderedGroup_Osemigroup__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20, clsrel_Ring__and__Field_Oordered__idom_1, clsarity_nat_23, clsrel_Ring__and__Field_Oidom_22, clsrel_Ring__and__Field_Oidom_5, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, clsrel_Ring__and__Field_Opordered__semiring_8, clsrel_OrderedGroup_Oab__group__add_3, clsrel_Ring__and__Field_Oring__1_12, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Ozdvd__0__left__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6, clsrel_Ring__and__Field_Olordered__ring_29, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, clsrel_Power_Orecpower_12, cls_Nat_Oadd__gr__0__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_1, clsarity_IntDef__Oint_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9, cls_Divides_Odvd__triv__left_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3, clsrel_Ring__and__Field_Oidom_19, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8, cls_Divides_Odvd__0__right_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22, clsrel_OrderedGroup_Olordered__ab__group__join_12, cls_IntDiv_Odvd__zminus__iff__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5, clsrel_Ring__and__Field_Ocomm__ring__1_11, clsrel_Ring__and__Field_Oordered__semidom_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsrel_Ring__and__Field_Oordered__idom_41, clsrel_Ring__and__Field_Osemiring__1__cancel_1, clsrel_Ring__and__Field_Oaxclass__abs__if_2, clsrel_Ring__and__Field_Oordered__ring__strict_9, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27, clsrel_Ring__and__Field_Oidom_3, clsrel_Ring__and__Field_Osemiring__1__cancel_2, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring_15, clsrel_Numeral_Onumber__ring_25, clsrel_Ring__and__Field_Osemiring__0__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15, clsrel_OrderedGroup_Olordered__ab__group__meet_7, cls_List_Olist_Odistinct__2__iff1_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Transitive__Closure_Or__into__rtrancl_0, clsrel_Numeral_Onumber__ring_0, clsrel_Ring__and__Field_Osemiring__1__cancel_11, clsrel_Ring__and__Field_Ocomm__semiring__0_9, clsarity_IntDef__Oint_10, clsrel_Ring__and__Field_Osemiring__0__cancel_2, clsrel_OrderedGroup_Olordered__ab__group_15, cls_Datatype__Universe_OdprodI_0, clsrel_OrderedGroup_Oab__group__add_2, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_List_Oappend__self__conv2__iff2_0, clsrel_Ring__and__Field_Oring_8, cls_List_Oappend__self__conv__iff2_0, cls_List_Oappend__same__eq__iff1_0, clsrel_Ring__and__Field_Oring_3, clsrel_Numeral_Onumber__ring_14, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Set_ODiffI_0, clsrel_OrderedGroup_Oab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__ring_20, clsrel_Ring__and__Field_Opordered__semiring_4, cls_Sum__Type_OInrI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3, clsarity_fun_1, clsrel_Ring__and__Field_Oring_11, cls_List_OlistsE_1, clsarity_nat_12, clsrel_Ring__and__Field_Oordered__ring__strict_17, clsrel_Ring__and__Field_Opordered__ring_4, clsrel_Ring__and__Field_Oordered__ring__strict_12, clsrel_OrderedGroup_Olordered__ab__group__join_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4, cls_Nat_OSuc__le__mono__iff2_0, clsrel_LOrder_Ojoin__semilorder_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_Set_OUn__empty__iff2_0, clsarity_IntDef__Oint_62, clsrel_Ring__and__Field_Oring__1_9, clsarity_IntDef__Oint_22, clsrel_OrderedGroup_Olordered__ab__group_10, clsrel_Ring__and__Field_Oordered__idom_30, cls_SetInterval_OgreaterThan__iff__iff1_0, clsarity_IntDef__Oint_5, clsrel_Ring__and__Field_Oring_12, cls_Set_OCompl__subset__Compl__iff__iff1_0, clsarity_nat_20, cls_Orderings_Oorder__less__irrefl__iff1_0, clsrel_Power_Orecpower_22, clsarity_IntDef__Oint_21, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1, clsrel_Ring__and__Field_Oordered__semiring__strict_14, clsarity_nat_5, cls_Datatype__Universe_Odsum__In1I_0, cls_Datatype__Universe_OuprodE_1, clsrel_Ring__and__Field_Oidom_30, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Ocomm__ring__1_18, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, clsrel_Ring__and__Field_Opordered__ring_8, clsrel_OrderedGroup_Opordered__ab__group__add_3, clsrel_Ring__and__Field_Osemiring__1_9, cls_List_Olistrel__Nil2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7, clsrel_OrderedGroup_Olordered__ab__group__join_4, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9, clsrel_LOrder_Olorder_1, cls_Relation_Orel__compI_0, clsarity_nat_42, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, clsrel_Ring__and__Field_Oordered__semidom_21, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Set_OUnionI_0, clsrel_Ring__and__Field_Oordered__idom_8, clsrel_Ring__and__Field_Osemiring__0_5, clsrel_OrderedGroup_Olordered__ab__group_11, clsrel_OrderedGroup_Olordered__ab__group__meet_3, clsrel_Ring__and__Field_Opordered__semiring_0, clsrel_OrderedGroup_Olordered__ab__group__abs_9, clsrel_Ring__and__Field_Opordered__comm__semiring_6, clsrel_Ring__and__Field_Ocomm__semiring__0_5, clsrel_OrderedGroup_Opordered__ab__semigroup__add_2, clsrel_Ring__and__Field_Ocomm__ring__1_22, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_14, clsrel_Ring__and__Field_Olordered__ring_6, clsrel_Ring__and__Field_Oordered__semiring__strict_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5, clsrel_Ring__and__Field_Oordered__semiring__strict_20, clsrel_Ring__and__Field_Ocomm__ring__1_9, clsrel_Ring__and__Field_Osemiring_3, clsrel_Numeral_Onumber__ring_3, clsarity_nat_31, cls_Datatype__Universe_OIn0__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_40, clsrel_OrderedGroup_Ocomm__monoid__add_3, clsrel_Ring__and__Field_Oordered__idom_25, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1, cls_Nat_OSuc__less__eq__iff1_0, cls_GCD_Ogcd__dvd2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23, clsrel_Power_Orecpower_8, cls_Relation_OdiagE_1, clsrel_Ring__and__Field_Oordered__ring__strict_0, clsarity_nat_9, clsrel_Ring__and__Field_Ocomm__ring__1_3, clsrel_Ring__and__Field_Opordered__semiring_11, clsrel_Ring__and__Field_Oordered__semidom_26, clsrel_Ring__and__Field_Ocomm__semiring__1_6, cls_IntDiv_Ozmod__eq__0D__dest_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18, clsrel_Ring__and__Field_Oordered__ring__strict_31, clsrel_Ring__and__Field_Oring__1_5, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, clsrel_Ring__and__Field_Oordered__idom_9, clsrel_Ring__and__Field_Osemiring__1_6, clsrel_Ring__and__Field_Ocomm__ring_5, clsrel_Ring__and__Field_Oidom_12, clsrel_Numeral_Onumber__ring_8, cls_Relation_OImage__singleton__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_10, clsrel_Ring__and__Field_Opordered__cancel__semiring_7, cls_List_ONil2__notin__lex__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Ocomm__semiring__1_9, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__ring__strict_34, clsrel_Ring__and__Field_Ocomm__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9, clsrel_Power_Orecpower_2, clsrel_Ring__and__Field_Olordered__ring_17, clsrel_Ring__and__Field_Oordered__semidom_15, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14, clsarity_nat_46, clsrel_Ring__and__Field_Oidom_16, cls_List_Oself__append__conv2__iff1_0, clsrel_Ring__and__Field_Olordered__ring_28, clsrel_Ring__and__Field_Oordered__semidom_5, clsrel_Ring__and__Field_Ocomm__semiring__0_1, clsrel_Ring__and__Field_Oordered__semidom_6, clsrel_Ring__and__Field_Oordered__semiring__strict_6, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_OrderedGroup_Opordered__ab__group__add_7, clsarity_IntDef__Oint_44, cls_Nat_Oneq0__conv__iff1_0, clsrel_Ring__and__Field_Oring_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, clsrel_Ring__and__Field_Opordered__ring_15, clsrel_Ring__and__Field_Olordered__ring_9, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, clsrel_OrderedGroup_Opordered__ab__group__add_5, clsrel_Ring__and__Field_Ocomm__semiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_22, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, clsrel_Ring__and__Field_Oordered__idom_33, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, clsrel_Ring__and__Field_Oordered__idom_44, clsrel_Ring__and__Field_Ocomm__semiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_37, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5, clsarity_nat_35, clsrel_Ring__and__Field_Oidom_8, clsrel_Ring__and__Field_Oidom_18, cls_List_Olist_Odistinct__1__iff1_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, clsrel_Ring__and__Field_Oordered__ring__strict_23, clsrel_Ring__and__Field_Oordered__semiring__strict_23, clsrel_Ring__and__Field_Oordered__ring__strict_29, clsrel_Ring__and__Field_Oordered__ring__strict_6, clsrel_Ring__and__Field_Oring__1_17, clsrel_OrderedGroup_Opordered__ab__group__add_13, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_Ring__and__Field_Opordered__comm__semiring_11, clsarity_IntDef__Oint_17, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3, cls_SetInterval_OatLeast__eq__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_12, clsrel_OrderedGroup_Olordered__ab__group_12, cls_Sum__Type_OPlusE_1, clsrel_Ring__and__Field_Oordered__semidom_29, clsrel_Ring__and__Field_Oordered__idom_0, cls_Set_OUnionE_0, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_Ring__and__Field_Osemiring__1_1, clsarity_IntDef__Oint_28, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, clsrel_Ring__and__Field_Osemiring__0_4, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_Divides_Odvd__1__left_0, cls_List_Oin__listsI_0, clsrel_Ring__and__Field_Ocomm__ring_7, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, clsrel_Ring__and__Field_Ocomm__ring_18, cls_IntDef_Onegative__zle_0, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, clsrel_Ring__and__Field_Oordered__idom_13, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Numeral_Onumber__ring_21, clsrel_Ring__and__Field_Oordered__idom_45, clsrel_OrderedGroup_Opordered__ab__group__add_0, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Power_Orecpower_20, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Oring__1_13, clsrel_Ring__and__Field_Osemiring__0__cancel_5, clsrel_OrderedGroup_Olordered__ab__group__join_10, clsarity_IntDef__Oint_41, clsrel_Ring__and__Field_Oordered__semiring__strict_0, clsarity_nat_24, cls_List_Oappend1__eq__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_0, clsrel_Ring__and__Field_Oidom_28, clsrel_Ring__and__Field_Oordered__idom_34, clsrel_Ring__and__Field_Osemiring_0, clsrel_Ring__and__Field_Opordered__ring_1, clsrel_Ring__and__Field_Oring_4, clsarity_IntDef__Oint_11, clsrel_Ring__and__Field_Oordered__semiring__strict_13, clsrel_Ring__and__Field_Opordered__semiring_9, clsrel_Ring__and__Field_Ocomm__semiring_3, clsrel_Ring__and__Field_Osemiring__1__cancel_8, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6, clsrel_Ring__and__Field_Olordered__ring_5, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsrel_Ring__and__Field_Oidom_27, clsrel_Ring__and__Field_Oordered__semidom_33, clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsrel_Ring__and__Field_Oidom_23, clsrel_Ring__and__Field_Olordered__ring_30, clsarity_nat_1, clsrel_Power_Orecpower_11, clsrel_Ring__and__Field_Oordered__idom_24, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, clsrel_LOrder_Omeet__semilorder_1, clsrel_Ring__and__Field_Oidom_4, clsarity_set_0, clsarity_IntDef__Oint_51, clsrel_Numeral_Onumber__ring_10, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0, cls_Nat_OSuc__not__Zero__iff1_0, clsrel_Numeral_Onumber__ring_26, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, clsarity_nat_4, clsrel_Ring__and__Field_Ocomm__ring__1_6, clsrel_Ring__and__Field_Opordered__ring_5, clsrel_Ring__and__Field_Oordered__idom_27, clsrel_Ring__and__Field_Oordered__ring__strict_13, clsrel_OrderedGroup_Opordered__ab__group__add_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, clsrel_Ring__and__Field_Opordered__ring_10, clsrel_Ring__and__Field_Olordered__ring_0, cls_Nat_Ole0_0, clsrel_OrderedGroup_Oab__semigroup__mult_1, cls_Nat_Oless__one__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_23, clsrel_Numeral_Onumber__ring_15, clsarity_IntDef__Oint_63, clsrel_Ring__and__Field_Oring__1_8, cls_Set_Osingleton__insert__inj__eq__iff1_0, clsarity_nat_19, cls_Sum__Type_OInl__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring_0, clsrel_Ring__and__Field_Oordered__semiring__strict_15, cls_Relation_OImage__singleton__iff__iff2_0, clsrel_Ring__and__Field_Olordered__ring_2, clsrel_Ring__and__Field_Ocomm__ring_14, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Osemiring__0__cancel_10, clsrel_Ring__and__Field_Oordered__semidom_30, clsrel_OrderedGroup_Ocomm__monoid__mult_4, clsrel_Ring__and__Field_Osemiring__1_5, clsrel_OrderedGroup_Olordered__ab__group__meet_8, clsrel_Ring__and__Field_Ocomm__semiring__0_8, cls_List_Olength__0__conv__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_5, clsrel_OrderedGroup_Omonoid__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2, clsrel_Ring__and__Field_Osemiring_4, clsarity_IntDef__Oint_12, clsrel_Ring__and__Field_Opordered__cancel__semiring_13, cls_Relation_OIdE_0, clsrel_Ring__and__Field_Oidom_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28, clsrel_Numeral_Onumber__ring_29, clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsarity_IntDef__Oint_55, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsrel_OrderedGroup_Opordered__ab__group__add_12, clsarity_IntDef__Oint_61, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_Numeral_Onumber__ring_9, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Olordered__ring_20, clsarity_IntDef__Oint_50, clsrel_Ring__and__Field_Opordered__ring_21, clsrel_Ring__and__Field_Ocomm__semiring__1_5, clsrel_OrderedGroup_Oab__group__add_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Oordered__idom_16, clsrel_Ring__and__Field_Osemiring__0_3, clsrel_OrderedGroup_Olordered__ab__group__join_5, clsrel_Ring__and__Field_Oring__1_16, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Numeral_Onumber__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Olordered__ring_16, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, clsrel_Ring__and__Field_Oring__1_3, cls_Set_OIntE_0, clsarity_nat_30, cls_Relation_Orel__compE_1, clsarity_set_4, clsrel_Ring__and__Field_Oring__1_10, cls_List_Oappend__is__Nil__conv__iff1_1, clsrel_Ring__and__Field_Oring__1_4, clsrel_Numeral_Onumber__ring_18, clsrel_Ring__and__Field_Ocomm__ring__1_17, clsrel_Ring__and__Field_Osemiring__0__cancel_0, clsrel_Ring__and__Field_Oordered__semidom_14, clsrel_Ring__and__Field_Oordered__ring__strict_2, clsarity_nat_41, clsrel_Ring__and__Field_Oordered__ring__strict_30, cls_Finite__Set_Ofinite__Un__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__abs_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__ring__1_28, clsrel_Ring__and__Field_Olordered__ring_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozminus__dvd__iff__iff2_0, clsarity_IntDef__Oint_9, clsrel_Ring__and__Field_Oordered__semiring__strict_18, clsrel_Ring__and__Field_Opordered__comm__semiring_4, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0, clsrel_Ring__and__Field_Olordered__ring_27, cls_Set_OinsertCI_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, clsrel_Ring__and__Field_Olordered__ring_13, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__ring_16, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0, clsrel_Power_Orecpower_19, clsrel_OrderedGroup_Olordered__ab__group__join_1, cls_List_Oappend__self__conv__iff1_0
% 10.34/3.39  % No. of inferences in proof: 2337
% 10.34/3.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2884 ms resp. 2310 ms w/o parsing
% 11.60/3.60  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.60/3.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------