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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SET822-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:31:00 AM UTC 2026

% Result   : Unsatisfiable 16.87s 5.88s
% Output   : Refutation 19.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1121
% Syntax   : Number of formulae    : 2243 ( 345 unt;   0 typ;   0 def)
%            Number of atoms       : 4225 ( 234 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 12458 (1986   ~;1982   |;   0   &;8490   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  162 ( 160 usr;  11 con; 0-6 aty)
%            Number of variables   : 3006 (   0   ^;3006   !;   0   ?;3006   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_P_decl,type,
    v_P: $i > $o ).

thf(v_f_decl,type,
    v_f: $i > $i ).

thf(v_b_decl,type,
    v_b: $i ).

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

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

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Osemiring__1__cancel_decl,type,
    class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_0_decl,type,
    c_0: $i ).

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

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__semiring__0__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

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

thf(c_Datatype__Universe_OIn1_decl,type,
    c_Datatype__Universe_OIn1: $i > $i > $i > $i ).

thf(c_Datatype__Universe_OIn0_decl,type,
    c_Datatype__Universe_OIn0: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

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

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

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

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

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

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

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

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

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

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

thf(c_Main_OdprodE__1_decl,type,
    c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__2_decl,type,
    c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__3_decl,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OdprodE__4_decl,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Main_OImageE__1_decl,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

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

thf(c_Main_Omod__eq__0D__dest__1_decl,type,
    c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).

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

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

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

thf(c_Main_OPlusE__1_decl,type,
    c_Main_OPlusE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OPlusE__2_decl,type,
    c_Main_OPlusE__2: $i > $i > $i > $i > $i ).

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

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

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

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

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

thf(c_Main_OUnionE__1_decl,type,
    c_Main_OUnionE__1: $i > $i > $i > $i ).

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

thf(c_Main_ORangeE__1_decl,type,
    c_Main_ORangeE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OsubsetI__1_decl,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_Main_OconverseE__1_decl,type,
    c_Main_OconverseE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OconverseE__2_decl,type,
    c_Main_OconverseE__2: $i > $i > $i > $i > $i ).

thf(c_Main_Oin__listsI__1_decl,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

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

thf(c_Main_OInterI__1_decl,type,
    c_Main_OInterI__1: $i > $i > $i > $i ).

thf(c_Main_OuprodE__1_decl,type,
    c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_OuprodE__2_decl,type,
    c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).

thf(c_Datatype_Oo2s_decl,type,
    c_Datatype_Oo2s: $i > $i > $i ).

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

thf(c_Main_Orel__compE__1_decl,type,
    c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_Orel__compE__3_decl,type,
    c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).

thf(c_1_decl,type,
    c_1: $i ).

thf(c_Main_Ofinite__Union__1_decl,type,
    c_Main_Ofinite__Union__1: $i > $i > $i ).

thf(c_Main_OdiagE__1_decl,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(c_Main_Orel__compE__2_decl,type,
    c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Main_OIdE__1_decl,type,
    c_Main_OIdE__1: $i > $i > $i ).

thf(c_Main_Ozmod__eq__0D__dest__1_decl,type,
    c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).

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

thf(c_Main_ODomainE__1_decl,type,
    c_Main_ODomainE__1: $i > $i > $i > $i > $i ).

thf(527,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).

thf(2163,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

thf(2630,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).

thf(1469,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).

thf(2778,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).

thf(1767,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).

thf(1559,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

thf(1729,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(1030,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).

thf(3167,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(674,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

thf(2463,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).

thf(1982,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(720,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(2559,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(585,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

thf(2280,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(944,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(3021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(2094,plain,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

thf(1411,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

thf(2889,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

thf(1823,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).

thf(2306,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(615,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

thf(2341,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(650,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

thf(2412,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(64,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(1237,plain,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ( A @ class_Numeral_Onumber )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

thf(2595,plain,
    ! [A: $i] :
      ( ( A @ class_Numeral_Onumber )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).

thf(1850,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(692,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(2499,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(32,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(1179,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

thf(2331,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

thf(1956,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

thf(1950,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

thf(1549,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

thf(1686,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(2250,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(1211,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(923,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

thf(2976,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(387,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

thf(1882,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).

thf(2622,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(890,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

thf(2908,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(1618,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(1205,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(166,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).

thf(1437,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

thf(1486,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(970,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

thf(3072,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

thf(2210,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

thf(2940,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(1596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

thf(2104,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

thf(2495,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(635,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

thf(2381,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(1443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(826,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).

thf(2776,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(767,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

thf(2659,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

thf(3040,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(1019,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

thf(3153,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(913,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

thf(2953,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

thf(1401,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(910,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

thf(2947,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(232,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).

thf(1569,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(569,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).

thf(2248,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(773,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(2671,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

thf(2676,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

thf(2014,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(586,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

thf(2282,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(1591,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

thf(2114,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(856,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

thf(2837,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(81,axiom,
    tc_nat @ class_Divides_Odiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(1269,plain,
    tc_nat @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(343,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(214,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).

thf(1533,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(1061,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(3217,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

thf(1608,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(997,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(3120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(12,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(1137,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

thf(1310,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1006,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(3135,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

thf(2918,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

thf(2184,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

thf(2316,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(902,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(2933,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).

thf(1327,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(76,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(1260,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

thf(1640,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(1954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

thf(2575,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(942,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

thf(3017,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(543,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(2195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).

thf(1705,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

thf(2607,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).

thf(2686,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(956,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

thf(3044,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

thf(1735,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(1275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).

thf(2141,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(661,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

thf(2434,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(1872,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

thf(2712,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(1085,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(3253,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

thf(1988,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(672,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

thf(2459,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

thf(1761,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).

thf(1342,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(201,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(1507,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(57,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(1222,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(624,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).

thf(2360,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(986,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).

thf(3103,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(364,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

thf(1835,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

thf(2020,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(451,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

thf(2010,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(272,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

thf(1650,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

thf(1359,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(1105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(3281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

thf(2082,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(706,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

thf(2531,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(872,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(2869,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(915,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

thf(2957,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(553,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(2216,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(1073,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).

thf(3236,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

thf(2432,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(688,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

thf(2491,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(4,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(1127,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(819,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(2763,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(926,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

thf(2985,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(142,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

thf(1391,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(1083,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(3249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(1441,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(1009,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(3140,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(1475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(532,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

thf(2173,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(1366,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(2400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

thf(1529,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).

thf(2067,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__ring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

thf(2825,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__ring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

thf(2819,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(348,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

thf(1803,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(398,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).

thf(1904,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).

thf(1703,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

thf(1482,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(1254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).

thf(1709,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(1101,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(3275,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(815,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).

thf(2755,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

thf(2708,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(693,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(2501,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).

thf(1860,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(778,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).

thf(2682,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(886,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(2897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(1992,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

thf(2126,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(764,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

thf(2654,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(261,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

thf(1628,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(1082,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(3248,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

thf(1409,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(1092,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(3263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(1063,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(3221,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

thf(2603,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).

thf(2916,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(1046,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(3195,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(948,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(3029,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

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

thf(2698,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(1004,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(3131,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

thf(1660,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).

thf(1298,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(994,axiom,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(3116,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).

thf(2667,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(614,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).

thf(2339,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(957,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(3046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

thf(1511,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(582,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(2274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).

thf(1577,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

thf(1455,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

thf(2562,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(979,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).

thf(3089,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

thf(2745,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

thf(2571,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(622,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

thf(2356,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

thf(1922,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(984,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).

thf(3099,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(866,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

thf(2857,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

thf(2169,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(17,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(1147,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(391,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

thf(1890,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(1060,axiom,
    tc_IntDef_Oint @ class_HOL_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(3216,plain,
    tc_IntDef_Oint @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).

thf(1741,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

thf(2024,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

thf(1773,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1036,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(3180,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(1071,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(3231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(707,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).

thf(2533,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(852,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

thf(2829,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).

thf(1545,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(654,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

thf(2420,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

thf(1892,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(136,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

thf(1379,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(69,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(1247,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(470,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(2049,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(700,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).

thf(2520,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(802,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

thf(2730,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

thf(2301,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(354,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

thf(1815,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).

thf(1494,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

thf(2989,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

thf(1362,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(1096,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(3268,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(1088,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

thf(3258,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

thf(1811,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

thf(2090,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

thf(1373,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).

thf(1978,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

thf(2034,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(1018,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(3152,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(482,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(2073,plain,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(534,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(2178,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

thf(2222,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).

thf(1946,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).

thf(1465,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

thf(1302,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

thf(1664,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(1113,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

thf(3295,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(829,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).

thf(2782,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(884,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

thf(2893,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

thf(1632,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

thf(2469,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(1026,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(3163,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(762,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

thf(2650,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

thf(2451,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(563,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

thf(2236,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(288,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).

thf(1682,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(11,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(1136,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(1858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(378,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

thf(1864,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).

thf(2122,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

thf(2254,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).

thf(1960,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).

thf(2555,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(981,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

thf(3093,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).

thf(1581,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).

thf(2335,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(696,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(2508,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = A )
      | ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(1169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

thf(1928,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(868,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).

thf(2861,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(952,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

thf(3036,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(514,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

thf(2137,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

thf(1351,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(163,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(1433,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

thf(1405,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

thf(2965,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

thf(1600,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

thf(1697,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(208,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(1521,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(796,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).

thf(2718,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(1038,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(3184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

thf(3068,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(1377,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(854,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

thf(2833,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(1042,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(3189,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
      | ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
      | ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

thf(1896,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).

thf(2190,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(171,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).

thf(1447,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).

thf(2483,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

thf(1622,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(656,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

thf(2424,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(824,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

thf(2772,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(1022,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).

thf(3157,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

thf(2002,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(1079,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(3243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
      | ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(842,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

thf(2809,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

thf(2242,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).

thf(2799,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(2286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(757,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

thf(2639,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(1067,axiom,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(3226,plain,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(1201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
       != ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(1070,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(3229,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(939,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

thf(3011,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(891,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

thf(2910,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

thf(2473,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).

thf(1306,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

thf(2364,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(505,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(2118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

thf(1338,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).

thf(1783,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(758,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).

thf(2641,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(380,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

thf(1868,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

thf(1604,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(897,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

thf(2922,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(1017,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(3151,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(983,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

thf(3097,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(1117,axiom,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(3301,plain,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

thf(2204,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(1093,axiom,
    tc_IntDef_Oint @ class_HOL_Oplus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(3265,plain,
    tc_IntDef_Oint @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(760,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

thf(2646,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(21,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(1153,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1039,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(3186,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

thf(2232,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(593,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(2296,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(961,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

thf(3054,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

thf(2061,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).

thf(2000,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).

thf(1636,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(663,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

thf(2441,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(733,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(2589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).

thf(2264,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(2805,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(711,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(2541,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(1519,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).

thf(1355,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(2,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( B @ ( A @ v_x ) @ c_in ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( B @ ( A @ v_x ) @ c_in ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(280,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).

thf(1666,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(921,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(2969,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(1076,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(3239,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(1072,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(3233,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(1020,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(3154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

thf(1370,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

thf(2032,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).

thf(2414,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(704,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(2528,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(1238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(1107,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

thf(3286,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(140,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).

thf(1387,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(396,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

thf(1900,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

thf(1723,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(1091,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(3261,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
      | ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(1223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(739,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).

thf(2601,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(658,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(2428,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(29,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(1174,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).

thf(1676,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).

thf(2133,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(53,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(1217,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

thf(2147,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

thf(1502,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(1054,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(3207,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(642,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).

thf(2396,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).

thf(2628,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

thf(1920,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(681,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).

thf(2477,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(1007,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(3137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(31,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(1178,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).

thf(1888,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

thf(1457,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(1012,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(3144,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

thf(1787,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(608,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(2327,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).

thf(2112,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).

thf(1573,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

thf(1423,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(1121,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(3307,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(1098,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(3271,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(1029,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(3166,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(665,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).

thf(2445,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(1043,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(3191,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

thf(1938,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

thf(2873,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

thf(1837,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(1097,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(3269,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1602,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

thf(1968,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(1049,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(3198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(769,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

thf(2663,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

thf(1555,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(356,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).

thf(1819,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

thf(1624,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(545,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

thf(2200,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).

thf(2609,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(48,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(1210,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).

thf(1656,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(959,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).

thf(3050,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(617,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

thf(2345,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
     != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

thf(1407,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(714,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

thf(2547,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(5,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(1128,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(86,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(1281,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

thf(2741,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

thf(1634,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

thf(2228,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(950,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(3033,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(401,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).

thf(1910,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(1936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(987,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

thf(3105,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).

thf(1541,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(524,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(2157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(2100,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(838,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(2801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

thf(2895,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(858,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).

thf(2841,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

thf(1375,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(727,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).

thf(2577,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).

thf(1970,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

thf(1856,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(283,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

thf(1672,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(996,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(3119,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(973,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).

thf(3078,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

thf(3001,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(1270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatMost ) )
       != ( A @ ( C @ c_SetInterval_OatMost ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(998,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

thf(3122,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(2692,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(1498,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(241,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

thf(1587,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(784,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).

thf(2694,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).

thf(1425,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

thf(1878,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

thf(2726,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(13,axiom,
    tc_nat @ class_HOL_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(1138,plain,
    tc_nat @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

thf(2724,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).

thf(1719,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).

thf(2537,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(1074,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(3237,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(324,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

thf(1755,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).

thf(2268,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(1053,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(3205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(964,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

thf(3060,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1034,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(3176,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(978,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

thf(3087,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).

thf(1397,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).

thf(1567,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

thf(1329,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1011,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(3143,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(126,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(1361,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(1035,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(3179,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(92,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(1292,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1056,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(3210,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

thf(2080,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(745,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

thf(2613,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

thf(1791,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(716,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(2551,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

thf(1644,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(1155,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

thf(1419,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(25,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(1160,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1010,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(3141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(876,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

thf(2877,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(428,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

thf(1964,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).

thf(1942,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).

thf(1739,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).

thf(1461,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(601,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

thf(2312,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

thf(2455,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

thf(2053,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

thf(2240,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

thf(1842,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(1214,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1045,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(3194,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

thf(2108,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

thf(2038,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).

thf(1612,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(924,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

thf(2978,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(1078,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(3242,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

thf(1539,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

thf(2851,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

thf(1799,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).

thf(1984,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(821,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

thf(2766,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).

thf(1715,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(966,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

thf(3064,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(581,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(2272,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

thf(1825,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(109,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(1324,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(694,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).

thf(2504,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(1150,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

thf(1478,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(71,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(1249,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(95,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(1297,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(1001,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(3126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

thf(1451,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

thf(2304,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(686,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

thf(2487,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(860,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

thf(2845,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(78,axiom,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(1266,plain,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

thf(2153,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(638,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

thf(2387,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).

thf(1831,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(1231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

thf(1668,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

thf(1974,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(38,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(1192,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

thf(1932,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(729,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

thf(2581,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

thf(2465,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1064,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

thf(3222,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

thf(2006,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(691,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

thf(2497,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

thf(1852,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

thf(2813,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

thf(1874,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(993,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).

thf(3115,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

thf(1429,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(1081,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(3247,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(989,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(3109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(971,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(3074,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

thf(3005,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(976,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).

thf(3083,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(1050,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(3201,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

thf(1759,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(1393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(2370,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).

thf(1525,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(1015,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(3147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(1333,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).

thf(1318,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(899,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

thf(2926,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

thf(1779,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

thf(2208,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).

thf(1695,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).

thf(1563,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(484,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

thf(2076,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(645,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).

thf(2402,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(1515,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(747,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

thf(2617,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

thf(1996,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(705,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(2529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).

thf(2749,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

thf(1434,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(788,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

thf(2702,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).

thf(2761,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

thf(2043,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(1104,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(3279,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(879,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

thf(2883,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(1033,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(3173,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).

thf(2057,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(1120,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(3306,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(369,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(1846,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(918,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

thf(2963,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(1286,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(2368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(648,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(2408,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

thf(2793,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).

thf(1616,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(931,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

thf(2995,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).

thf(1906,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(1727,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(1003,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(3130,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(591,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

thf(2292,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

thf(2149,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(1273,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

thf(1747,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(1110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(3289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).

thf(2936,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(10,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).

thf(1135,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

thf(1648,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(640,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

thf(2391,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).

thf(2904,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

thf(1680,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(955,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).

thf(3042,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(731,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

thf(2585,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(1087,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(3257,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(55,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(1219,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).

thf(2028,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

thf(2734,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(990,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(3111,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1100,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(3274,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(702,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

thf(2524,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(632,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(2376,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(1023,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(3158,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(575,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(2260,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(22,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1154,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(1040,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).

thf(3187,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(363,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

thf(1833,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(969,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).

thf(3070,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).

thf(1916,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).

thf(1884,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(1389,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

thf(2791,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(832,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

thf(2789,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

thf(2188,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(641,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(2393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
        = ( C @ ( A @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

thf(1652,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(1099,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(3272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(148,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

thf(1403,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).

thf(2716,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(846,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

thf(2817,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(3,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ v_x ) @ v_P )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ v_x ) @ v_P )
      | ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

thf(2827,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(867,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(2859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(905,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

thf(2938,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(766,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

thf(2657,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).

thf(2849,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(1620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(687,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).

thf(2489,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(1106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(3283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(1094,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(3266,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(774,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(2674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).

thf(2016,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(215,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

thf(1535,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(929,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(2991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(344,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

thf(1795,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

thf(1701,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

thf(2398,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(1488,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(916,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

thf(2959,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(1058,axiom,
    tc_IntDef_Oint @ class_HOL_Otimes,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(3213,plain,
    tc_IntDef_Oint @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(14,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(1139,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(2220,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

thf(1707,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

thf(1312,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(806,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(2738,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

thf(1733,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(999,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(3123,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).

thf(2055,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(790,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

thf(2706,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(329,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).

thf(1765,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(1119,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(3304,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(980,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

thf(3091,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(1118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(3302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

thf(1638,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(1032,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(3170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
      | ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(1065,axiom,
    tc_IntDef_Oint @ class_HOL_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(3223,plain,
    tc_IntDef_Oint @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

thf(2161,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

thf(2193,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).

thf(3023,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(883,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

thf(2891,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

thf(2308,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(817,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(2759,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(814,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

thf(2753,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(671,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(2457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(719,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

thf(2557,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(725,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

thf(2573,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(623,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

thf(2358,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(40,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(1194,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(985,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

thf(3101,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(47,axiom,
    tc_nat @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(1209,plain,
    tc_nat @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

thf(2151,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

thf(2906,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(1,negated_conjecture,
    v_b @ v_f @ v_P,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1122,plain,
    v_b @ v_f @ v_P,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(1025,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(3160,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(1084,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(3251,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

thf(2084,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(1075,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(3238,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).

thf(2214,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(636,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).

thf(2383,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(751,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).

thf(2624,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(927,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

thf(2987,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).

thf(1894,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(689,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(2493,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(655,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

thf(2422,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(953,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

thf(3038,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(756,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

thf(2637,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(825,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

thf(2774,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(1108,axiom,
    tc_IntDef_Oint @ class_Divides_Odiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(3287,plain,
    tc_IntDef_Oint @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(242,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).

thf(1589,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

thf(2284,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).

thf(1492,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(594,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

thf(2299,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(914,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

thf(2955,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(568,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).

thf(2246,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(772,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(2669,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(15,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(1144,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

thf(2116,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(857,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).

thf(2839,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

thf(1771,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(909,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(2945,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
      | ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(1048,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(3197,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

thf(1801,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(633,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(2378,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(967,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).

thf(3066,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(292,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

thf(1690,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1037,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(3182,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

thf(2871,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(167,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

thf(1439,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

thf(2065,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(1175,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(536,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).

thf(2182,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).

thf(1471,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(755,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(2632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
       != ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

thf(1557,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(262,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

thf(1630,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).

thf(2780,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(2757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(735,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).

thf(2593,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).

thf(1344,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

thf(2252,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(792,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

thf(2710,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

thf(1688,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(741,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).

thf(2605,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(947,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

thf(3027,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(602,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).

thf(2314,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).

thf(2343,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

thf(1821,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).

thf(1731,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(1028,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(3165,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

thf(1862,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(951,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

thf(3034,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(649,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(2410,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

thf(1325,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(19,axiom,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(1149,plain,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1115,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(3298,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(93,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(1293,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

thf(2278,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(717,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

thf(2553,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(900,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(2928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( B @ c_insert ) ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

thf(1381,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(673,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

thf(2461,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(922,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(2974,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).

thf(2329,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(1198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(409,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

thf(1926,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

thf(2350,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).

thf(2086,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

thf(2139,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1024,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(3159,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

thf(2022,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

thf(2535,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(933,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

thf(2999,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

thf(1805,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(2506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

thf(2770,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

thf(2418,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(244,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

thf(1594,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

thf(1699,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).

thf(2212,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(531,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

thf(2171,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(50,axiom,
    tc_nat @ class_Numeral_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(1213,plain,
    tc_nat @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

thf(2835,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).

thf(2051,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

thf(2481,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

thf(1445,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(749,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

thf(2620,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(901,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(2931,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(589,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

thf(2288,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(1077,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(3241,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(2797,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(334,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

thf(1775,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

thf(2244,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

thf(1364,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

thf(2967,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).

thf(1496,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(596,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(2303,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(480,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

thf(2069,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(871,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(2867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

thf(1413,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(1948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).

thf(1809,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(27,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(1166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(46,axiom,
    tc_nat @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(1208,plain,
    tc_nat @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

thf(2665,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

thf(1467,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).

thf(1684,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(1340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(1112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(3292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
      | ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(1181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

thf(1551,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(260,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

thf(1626,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(938,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

thf(3009,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

thf(1583,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

thf(2914,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(949,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

thf(3031,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

thf(1662,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(494,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(2096,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

thf(1304,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1044,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

thf(3193,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

thf(2318,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).

thf(2784,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(763,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(2652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(678,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).

thf(2471,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

thf(2124,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(562,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

thf(2234,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(9,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(1134,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1014,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(3146,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(667,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(2449,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(202,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).

thf(1509,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(958,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).

thf(3048,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(779,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(2684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

thf(2202,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

thf(2333,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(1145,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(2256,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(722,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(2564,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(1103,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(3278,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).

thf(2597,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(1958,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(2942,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(698,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(2513,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).

thf(1547,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(991,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(3112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(768,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(2661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(318,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(1743,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(1059,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(3214,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(1090,axiom,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(3260,plain,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

thf(2720,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).

thf(1531,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

thf(2831,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(869,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).

thf(2863,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(246,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).

thf(1598,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(975,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(3082,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(541,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(2192,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

thf(2143,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(2012,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(2732,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(72,axiom,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(1252,plain,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(776,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

thf(2678,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(699,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).

thf(2518,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).

thf(1368,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1069,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(3228,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(2175,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(848,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(2821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(1055,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

thf(3209,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

thf(1753,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(79,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(1267,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

thf(3058,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(61,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(1230,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

thf(1484,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(492,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(2092,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(557,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

thf(2224,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

thf(2165,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

thf(2920,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(787,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).

thf(2700,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(1051,axiom,
    tc_IntDef_Oint @ class_Power_Orecpower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(3202,plain,
    tc_IntDef_Oint @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

thf(1785,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

thf(2337,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).

thf(1763,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

thf(1336,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(56,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(1220,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

thf(2354,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(765,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(2656,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

thf(1711,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

thf(3019,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(974,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(3080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
      | ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(811,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

thf(2747,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(723,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

thf(2569,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(1080,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

thf(3246,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

thf(1813,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(1300,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(992,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(3114,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

thf(2688,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

thf(2276,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(436,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

thf(1980,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

thf(2128,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

thf(1658,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(606,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(2322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

thf(2545,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

thf(2599,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(1130,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

thf(1579,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(88,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(1285,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(54,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(1218,plain,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(982,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

thf(3095,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

thf(1934,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(634,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

thf(2379,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(712,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

thf(2543,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(2579,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(199,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).

thf(1504,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(1109,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

thf(3288,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

thf(1543,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(988,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

thf(3107,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(395,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

thf(1898,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(1257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1000,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(3124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).

thf(2426,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(122,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).

thf(1353,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(859,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

thf(2843,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(518,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

thf(2145,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(432,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

thf(1972,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

thf(2320,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(200,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1506,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

thf(1749,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(1066,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(3224,plain,
    ! [B: $i,A: $i] :
      ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

thf(1427,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(240,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).

thf(1585,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

thf(2511,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).

thf(1670,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).

thf(1797,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(995,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(3117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).

thf(2949,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

thf(2722,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(801,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(2728,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(305,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

thf(1717,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

thf(2030,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(132,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(1372,plain,
    ! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1086,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

thf(3256,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(841,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

thf(2807,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(1021,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(3156,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(937,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

thf(3007,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(578,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

thf(2266,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(682,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).

thf(2479,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

thf(2088,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(33,axiom,
    tc_nat @ class_Power_Orecpower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(1180,plain,
    tc_nat @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(429,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(1966,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

thf(2885,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(355,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).

thf(1817,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(1041,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(3188,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(206,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).

thf(1517,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).

thf(1807,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).

thf(1998,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

thf(2865,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

thf(2875,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(1031,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(3168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(416,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

thf(1940,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(1421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

thf(2924,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(1839,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(1008,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

thf(3139,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

thf(2626,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(1918,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).

thf(1316,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).

thf(2352,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).

thf(1459,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).

thf(2045,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(785,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

thf(2696,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).

thf(1553,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(1157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

thf(2078,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).

thf(2310,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(368,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(1844,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(618,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(2347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(274,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(1654,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

thf(2611,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

thf(2325,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(1781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(52,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(1216,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).

thf(2743,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(932,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(2997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(36,axiom,
    tc_nat @ class_HOL_Otimes,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(1189,plain,
    tc_nat @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

thf(2110,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

thf(1575,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(1289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(962,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

thf(3056,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(558,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(2226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
      | ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

thf(1453,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(759,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(2643,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

thf(1866,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

thf(2071,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

thf(2591,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(73,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(1253,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

thf(2167,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

thf(2389,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).

thf(2098,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(1745,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

thf(2026,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(1854,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(977,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

thf(3085,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(270,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

thf(1646,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(664,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).

thf(2443,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

thf(1385,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

thf(1721,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

thf(1674,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(865,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

thf(2855,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(864,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

thf(2853,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(590,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

thf(2290,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(513,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

thf(2135,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

thf(2406,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(849,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

thf(2823,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(1062,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(3220,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

thf(2811,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

thf(2004,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(935,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(3003,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(67,axiom,
    tc_nat @ class_HOL_Oplus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(1244,plain,
    tc_nat @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(820,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(2764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

thf(1523,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
     != ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(703,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

thf(2526,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(652,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

thf(2416,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

thf(2934,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

thf(2262,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(892,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).

thf(2912,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(1016,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(3149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(39,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(1193,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).

thf(2362,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(777,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(2680,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).

thf(1513,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(807,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

thf(2739,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).

thf(1994,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(254,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(1614,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(666,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

thf(2447,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(908,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(2944,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(2475,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(831,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(2786,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

thf(2648,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(335,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).

thf(1777,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(1095,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).

thf(3267,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).

thf(1308,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(544,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

thf(2198,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).

thf(2902,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).

thf(2120,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

thf(2230,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(592,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).

thf(2294,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(464,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).

thf(2036,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

thf(1908,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

thf(2374,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).

thf(2155,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(1111,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(3291,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(732,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

thf(2587,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(60,axiom,
    tc_nat @ class_LOrder_Olorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(1229,plain,
    tc_nat @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

thf(1395,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(701,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(2522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

thf(2951,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(384,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).

thf(1876,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).

thf(1757,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(1027,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(3164,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).

thf(2218,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).

thf(2258,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(8,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(1133,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(1642,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(497,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

thf(2102,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).

thf(1725,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(85,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(1280,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

thf(2385,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

thf(1678,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(845,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).

thf(2815,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(805,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

thf(2736,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).

thf(2008,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

thf(1986,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(1527,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(18,axiom,
    tc_nat @ class_HOL_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(1148,plain,
    tc_nat @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(3132,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(70,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(1248,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(822,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(2768,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(187,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

thf(1480,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(1052,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(3203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

thf(3062,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(1013,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

thf(3145,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(941,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).

thf(3015,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(165,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

thf(1436,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(813,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).

thf(2751,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

thf(1314,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(341,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

thf(1789,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

thf(2366,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(646,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

thf(2404,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(748,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(2619,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(466,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(2040,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

thf(2549,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(538,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(2186,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(1102,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(3277,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(1561,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(789,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

thf(2704,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(917,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

thf(2961,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(90,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(1288,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).

thf(2714,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(1047,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(3196,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(835,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

thf(2795,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

thf(1473,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(1346,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

thf(2063,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

thf(1610,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).

thf(1930,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(63,axiom,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(1236,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(525,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

thf(2159,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(676,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

thf(2467,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

thf(1976,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

thf(1500,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

thf(2372,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(1002,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(3128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

thf(1829,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(6,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(1129,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(946,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(3025,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(1827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(1261,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
       != ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(659,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

thf(2430,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(80,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(1268,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(839,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(2803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

thf(2847,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(685,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

thf(2485,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

thf(1537,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

thf(1357,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(730,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

thf(2583,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(1089,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(3259,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(710,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(2539,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

thf(1713,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

thf(1880,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

thf(1431,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

thf(3076,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

thf(1902,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(1399,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(2270,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(940,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

thf(3013,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(2879,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).

thf(1320,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(1962,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(878,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

thf(2881,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(2018,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(662,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(2436,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

thf(2106,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(1114,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(3296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

thf(1331,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(1606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
      | ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1068,axiom,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(3227,plain,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(1944,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(1057,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(3212,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(3299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

thf(2206,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

thf(1737,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(881,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

thf(2887,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(35,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(1184,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).

thf(2074,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(782,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

thf(2690,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).

thf(1463,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

thf(1565,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

thf(1848,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

thf(2059,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(564,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).

thf(2238,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

thf(1490,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

thf(2615,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

thf(1769,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(669,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).

thf(2453,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

thf(3052,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(930,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(2993,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(44,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(1204,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).

thf(1449,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

thf(1912,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(925,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(2980,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

thf(1417,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(381,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

thf(1870,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(3385,plain,
    $false,
    inference(e,[status(thm)],[2163,2630,1469,2778,1767,1559,1729,3167,2463,1982,2559,2280,3021,1322,2094,1411,2889,1823,1190,2306,2341,2412,1237,2595,1850,2499,1179,2331,1956,1950,1549,1686,2250,1211,2976,1882,2622,2908,1618,1205,1692,1437,1486,3072,1924,2210,2940,1596,2104,2495,2381,1443,2776,2659,3040,3153,2953,1401,2947,1569,2248,2671,2676,2014,2282,1591,2114,2837,1269,1793,1533,3217,1608,3120,1137,1310,3135,2918,2184,2316,2933,1327,1260,1640,1954,2575,3017,2195,1705,2607,2686,3044,1735,1275,2141,2434,1872,2712,3253,1988,2459,1761,1342,1507,1222,2360,3103,1835,2020,2010,1650,1359,3281,2082,2531,2869,2957,2216,3236,2432,1914,2491,1127,2763,2985,1391,3249,1441,3140,1475,2173,1366,2400,1529,2067,2825,2819,1803,1904,1703,1482,1254,1709,3275,2755,2708,2501,1860,2682,2897,1992,2126,2654,1628,3248,1409,3263,3221,2603,2916,3195,3029,2698,3131,1660,1298,3116,2667,2339,3046,1511,2274,1577,1455,2562,3089,2745,2571,2356,1922,3099,2857,2169,1147,1890,3216,1741,2024,1773,3180,3231,2533,2829,1545,2420,1892,1379,1247,2049,2520,2730,2301,1815,1494,2989,1362,3268,3258,1415,1811,2090,1373,1978,2034,3152,2073,2178,2222,1946,1465,1302,1664,3295,2782,2893,1632,2469,3163,2650,2451,2236,1682,1136,1858,1864,2122,1383,2254,1960,2555,3093,1581,2335,2508,1169,1928,2861,1886,3036,2137,1351,1433,1405,2965,1600,1697,1521,2718,3184,3068,1377,2833,3189,1896,2190,1447,2483,1622,2424,2772,3157,2002,3243,2809,2242,2799,2286,2639,3226,1201,3229,3011,2910,2473,1306,2364,2118,1338,2047,1783,2641,1868,1163,1604,2922,3151,3097,3301,2204,3265,2646,1153,3186,2232,2296,3054,2061,2000,1636,2441,2589,2264,2805,2541,1519,1355,1123,1666,2969,3239,3233,3154,1370,2032,2414,2528,1238,3286,1387,1900,1723,3261,1223,2601,2428,1174,1676,2133,1217,2147,1502,1751,3207,2396,2628,1920,2477,3137,1178,1888,1457,3144,1787,2327,2112,1573,1423,3307,3271,3166,2445,3191,1938,2873,1837,3269,1602,1968,3198,2663,1555,1819,1624,2200,2609,1210,1656,3050,2345,1195,1407,2547,1128,1281,2741,1634,2228,3033,1910,1936,3105,1541,2157,2100,2801,2895,2841,1375,2577,1970,1856,1672,3119,3078,3001,1270,3122,2692,1498,1587,2694,1425,1878,2726,1138,2724,1719,2537,3237,1755,2268,3205,3060,3176,3087,1397,1567,1329,3143,1361,3179,1292,3210,2080,2613,1791,2551,1644,1155,1419,1160,3141,2877,1964,1942,1739,1461,2312,2455,2053,2240,1842,1214,3194,2108,2038,1612,2978,3242,1539,2851,1799,1984,2766,1715,3064,2272,1825,1324,2504,1150,1478,1249,1297,3126,1451,2304,2487,2845,1266,2153,2387,1831,1231,1668,1974,1192,1932,2581,2465,3222,2006,2497,1852,2813,1874,3115,1429,3247,3109,3074,3005,3083,3201,1759,1393,2370,1525,3147,1333,1318,2926,1779,2208,1695,1563,2076,2402,1515,2617,1996,2529,2749,1434,1241,2702,2761,2043,3279,2883,3173,2057,3306,1846,2963,1286,2368,2408,2793,1616,2995,1906,1727,3130,2292,2149,1273,1747,3289,2936,1135,1648,2391,2904,1680,3042,2585,3257,1219,2028,2734,3111,3274,2524,2376,3158,2260,1154,3187,1833,3070,1916,1884,1389,2791,2789,2188,2393,1652,3272,1403,2716,2817,1124,2827,2859,2938,2657,2849,1620,2489,3283,3266,2674,2016,1535,2991,1795,1701,2398,1226,1488,2959,3213,1139,2220,1707,1312,2738,1733,3123,2055,2706,1765,3304,3091,3302,1638,3170,3223,2161,2193,3023,2891,2308,2759,2753,2457,2557,2573,2358,1194,3101,1209,2151,2906,1122,3160,1282,3251,2084,3238,2214,2383,2624,2987,1894,2493,2422,3038,2637,2774,3287,1589,2284,1492,2299,2955,2246,2669,1144,2116,2839,1771,2945,3197,1801,2378,3066,1690,3182,1571,2871,1439,2065,1175,2180,2182,1471,2632,1557,1630,2780,2757,2593,1344,2252,2710,1688,2605,3027,2314,2343,1821,1731,3165,1862,3034,2410,1325,1149,3298,1293,2278,2553,2928,1381,2461,2974,2329,1952,1198,1926,2350,2086,2139,3159,2022,2535,2999,1805,2506,2770,2418,1594,1699,2212,2171,1213,2835,2051,1245,2481,1445,2620,2931,2288,3241,2797,1775,2244,1364,2967,1496,2303,2069,2867,1413,1948,1809,1166,1208,2665,1467,1684,1340,3292,1181,1551,1626,3009,1583,2914,3031,1662,2096,1304,3193,2318,2784,2652,2471,2124,2234,1134,3146,2449,1509,1990,3048,2684,2202,2333,1145,2256,2564,3278,2597,1958,2942,2513,1547,3112,2661,1743,3214,3260,2720,1531,2831,2863,1598,3082,2192,2143,2012,2732,1252,2678,2518,1368,3228,2175,2821,3209,1753,1267,3058,1230,1484,2092,2224,2165,2920,2700,3202,1785,2337,1763,1336,1220,2354,2656,1711,3019,3080,2747,2569,3246,1813,1300,3114,2688,2276,1980,2128,1658,2322,2545,2599,1130,1579,1285,1218,3095,1934,2379,2543,2579,1504,3288,1543,3107,1898,1257,3124,2426,1353,2843,2145,1972,2320,1506,1749,3224,1427,1585,2511,1670,1797,3117,2949,2722,2728,1717,2030,1372,3256,2807,3156,3007,2266,2479,2088,1180,1966,2885,1817,3188,1517,1807,1998,2865,2875,3168,1940,1421,2924,1839,3139,2626,1918,1316,2352,1459,2045,2696,1553,1157,2078,2310,1844,2347,1654,2611,2325,1781,1216,2743,2997,1189,2110,1575,1289,3056,2226,1453,2643,1866,2071,2591,1253,2167,2389,2098,1745,2026,1854,3085,1646,2443,1385,1721,1674,2855,2853,2290,2135,2406,2823,3220,2811,2004,3003,1244,2764,1523,2130,2526,2416,2934,2262,2912,3149,1193,2362,2680,1513,2739,1994,1614,2447,2944,2475,2786,2648,1777,3267,1294,1308,2198,2902,2120,2230,2294,2036,1908,2374,2155,3291,2587,1229,1395,2522,2951,1876,1757,3164,2218,2258,1133,1642,2102,1725,1280,2385,1678,2815,2736,2008,1986,1527,1148,3132,1248,2768,1480,3203,3062,3145,3015,1436,2751,1314,1789,2366,2404,2619,2040,2549,2186,3277,1561,2704,2961,1288,2714,3196,2795,1473,1346,2063,1610,1930,1236,2159,2467,1976,1500,2372,3128,1829,1129,3025,1827,1261,2430,1268,2803,2847,2485,1537,1357,2583,3259,2539,1713,1880,1431,3076,1902,1399,2270,3013,2879,1320,1962,2881,2018,2436,2106,3296,1331,1606,3227,1944,3212,3299,2206,1737,2887,1184,2074,2690,1463,1565,1848,2059,2238,1490,2615,1769,2453,3052,2993,1204,1449,1912,2980,1417,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET822-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.60  % Computer : n004.cluster.edu
% 0.12/0.60  % Model    : x86_64 x86_64
% 0.12/0.60  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60  % Memory   : 8046.5625MB
% 0.12/0.60  % OS       : Linux 6.8.0-71-generic
% 0.12/0.60  % CPULimit : 300
% 0.12/0.60  % WCLimit  : 300
% 0.12/0.60  % DateTime : Sat Sep 26 08:18:38 UTC 2026
% 0.12/0.60  % CPUTime  : 
% 0.12/0.60  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.19  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.79/1.58  % [INFO] 	 Parsing done (383ms). 
% 1.79/1.59  % [INFO] 	 Running in sequential loop mode. 
% 2.85/1.97  % [INFO] 	 eprover registered as external prover. 
% 2.85/1.98  % [INFO] 	 Scanning for conjecture ... 
% 3.41/2.17  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ... 
% 4.83/2.53  % [INFO] 	 Axiom selection finished. Selected 1118 axioms (removed 239 axioms). 
% 5.49/2.76  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.49/2.77  % [INFO] 	 Type checking passed. 
% 5.49/2.78  % [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 ... 
% 16.87/5.86  % External prover 'e' found a proof!
% 16.87/5.86  % [INFO] 	 Killing All external provers ... 
% 16.87/5.86  % Time passed: 5113ms (effective reasoning time: 4264ms)
% 16.87/5.88  % Axioms used in derivation (1118): 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_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, 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, 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, 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_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, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring_9, cls_SetInterval_Ofinite__atLeastLessThan__int_0, 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, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, clsrel_Ring__and__Field_Oidom_1, 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_Sum__Type_OPlusE_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_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, clsrel_Ring__and__Field_Oordered__idom_49, clsrel_Numeral_Onumber__ring_19, 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_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, 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, 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, clsrel_Ring__and__Field_Opordered__semiring_1, 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_Oring_5, 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, 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_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, clsrel_Ring__and__Field_Oordered__idom_29, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_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_List_Oin__listsI_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, clsrel_Ring__and__Field_Ocomm__ring__1_8, clsrel_LOrder_Olorder_0, clsrel_Ring__and__Field_Oidom_2, 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, 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_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, 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__1__cancel_0, 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, 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__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_Osemiring__0_1, 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_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, 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, 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_Power_Orecpower_12, clsrel_Ring__and__Field_Oidom_5, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_Ring__and__Field_Opordered__comm__semiring_1, 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, 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, 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, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4, cls_List_Oappend__self__conv__iff2_0, clsrel_Ring__and__Field_Oordered__idom_30, 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_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, clsarity_IntDef__Oint_5, clsrel_Ring__and__Field_Oring_12, cls_Set_OCompl__subset__Compl__iff__iff1_0, clsarity_nat_20, 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, 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, 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, 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_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_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_Oordered__comm__semiring__strict_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_OrderedGroup_Oab__semigroup__mult_1, 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_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, 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, 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_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_Opordered__cancel__comm__semiring_0, 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_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, 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
% 16.87/5.88  % No. of inferences in proof: 2243
% 16.87/5.88  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5113 ms resp. 4264 ms w/o parsing
% 19.13/6.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.13/6.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------