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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n018.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 08:30:59 AM UTC 2026

% Result   : Unsatisfiable 16.73s 4.84s
% Output   : Refutation 18.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1170
% Syntax   : Number of formulae    : 2341 ( 389 unt;   0 typ;   0 def)
%            Number of atoms       : 4393 ( 268 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 13200 (2066   ~;2052   |;   0   &;9082   @)
%                                         (   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     :  168 ( 166 usr;  14 con; 0-6 aty)
%            Number of variables   : 3168 (   0   ^;3168   !;   0   ?;3168   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_less_decl,type,
    c_less: $i > $i > $i > $o ).

thf(v_a_decl,type,
    v_a: $i ).

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

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

thf(v_c_decl,type,
    v_c: $i ).

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

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

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

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

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_Wellfounded__Recursion_Owf_decl,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

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

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

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

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

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

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(c_Nat_Osize_decl,type,
    c_Nat_Osize: $i > $i > $i ).

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

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

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

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

thf(tc_set_decl,type,
    tc_set: $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_Osemiring__0_decl,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Osemiring_decl,type,
    class_Ring__and__Field_Osemiring: $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_Ocomm__semiring__1__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $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(class_OrderedGroup_Osemigroup__add_decl,type,
    class_OrderedGroup_Osemigroup__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(class_OrderedGroup_Ocomm__monoid__add_decl,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

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

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

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

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

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

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

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

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

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

thf(class_Power_Orecpower_decl,type,
    class_Power_Orecpower: $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_Ocomm__semiring__1_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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_Oaxclass__0__neq__1_decl,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_minus_decl,type,
    c_minus: $i > $i > $i > $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_SetInterval_OlessThan_decl,type,
    c_SetInterval_OlessThan: $i > $i > $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_SetInterval_OgreaterThan_decl,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

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

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

thf(c_Relation_Otrans_decl,type,
    c_Relation_Otrans: $i > $i > $o ).

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

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(720,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(2630,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)],[720]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

thf(1718,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

thf(2094,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)],[454]) ).

thf(845,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).

thf(2876,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(868,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

thf(2921,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)],[868]) ).

thf(1130,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

thf(3397,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

thf(1840,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(623,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

thf(2427,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

thf(2544,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)],[679]) ).

thf(575,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).

thf(2331,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(247,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(1686,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(918,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

thf(3021,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)],[918]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ tc_set @ ( A @ c_uminus ) )
       != ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(1322,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)],[60]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

thf(1665,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)],[236]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).

thf(1586,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)],[196]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(1501,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(710,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(2612,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

thf(1469,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(776,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(2744,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)],[776]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(1369,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

thf(2295,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)],[556]) ).

thf(935,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

thf(3053,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)],[935]) ).

thf(1098,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(3345,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)],[1098]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

thf(2341,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

thf(2109,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)],[461]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).

thf(2131,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

thf(1454,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(2031,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

thf(2072,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(1767,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(1132,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(3399,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

thf(1995,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).

thf(1315,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

thf(2787,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)],[798]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

thf(1850,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)],[331]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

thf(2499,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(686,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).

thf(2559,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(1165,axiom,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(3449,plain,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(1956,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(380,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

thf(1950,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(2280,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

thf(1554,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)],[179]) ).

thf(993,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

thf(3172,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(1200,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)],[13]) ).

thf(1000,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

thf(3185,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)],[1000]) ).

thf(1078,axiom,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(3317,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(716,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

thf(2622,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

thf(2062,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)],[438]) ).

thf(983,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

thf(3153,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)],[983]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

thf(1401,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)],[100]) ).

thf(955,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(3098,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

thf(1728,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

thf(2282,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(464,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).

thf(2114,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).

thf(1692,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ( tc_IntDef_Oint @ ( A @ ( v_a @ c_in ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( v_b @ c_in ) ) )
      | ( tc_IntDef_Oint @ ( A @ ( v_c @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(1173,plain,
    ! [A: $i] :
      ( ( tc_IntDef_Oint @ ( A @ ( v_a @ c_in ) ) )
      | ~ ( tc_IntDef_Oint @ ( A @ ( v_b @ c_in ) ) )
      | ( tc_IntDef_Oint @ ( A @ ( v_c @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(563,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

thf(2309,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)],[563]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

thf(2976,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)],[896]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

thf(3072,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

thf(1924,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)],[367]) ).

thf(878,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).

thf(2940,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

thf(1406,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)],[103]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

thf(1290,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)],[43]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

thf(1882,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).

thf(2808,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(1522,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(727,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

thf(2644,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(658,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

thf(2495,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)],[658]) ).

thf(1023,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(3230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

thf(2381,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

thf(2659,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)],[734]) ).

thf(1146,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(3417,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)],[1146]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1618,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(1059,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(3285,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

thf(1422,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(187,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(1569,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).

thf(1939,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

thf(2671,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)],[740]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).

thf(1544,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(914,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(3012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

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

thf(1205,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)],[14]) ).

thf(391,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).

thf(1971,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(1135,axiom,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(3402,plain,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(2854,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)],[833]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

thf(1533,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)],[168]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

thf(1426,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

thf(1671,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1159,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(3439,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(1655,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(933,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).

thf(3049,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)],[933]) ).

thf(709,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/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(2607,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)],[709]) ).

thf(53,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/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(1310,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)],[53]) ).

thf(974,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).

thf(3135,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(930,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(3044,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)],[930]) ).

thf(23,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(1233,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)],[23]) ).

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

thf(1327,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)],[62]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

thf(1640,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)],[223]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).

thf(1458,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)],[130]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).

thf(1497,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(916,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

thf(3017,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(2195,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

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

thf(1705,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

thf(2035,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)],[424]) ).

thf(1089,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(3332,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(1113,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(3367,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)],[1113]) ).

thf(1112,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(3365,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)],[1112]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

thf(2740,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(405,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(1999,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1163,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(3446,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(634,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(2448,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)],[634]) ).

thf(1093,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(3338,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)],[1093]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

thf(2933,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(38,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(1275,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)],[38]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(2141,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(341,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(1872,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)],[341]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

thf(2712,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)],[761]) ).

thf(492,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).

thf(2168,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

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

thf(1260,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)],[33]) ).

thf(1038,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(3253,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)],[1038]) ).

thf(640,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

thf(2459,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(1144,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(3414,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)],[1144]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).

thf(1761,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).

thf(1342,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(967,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

thf(3121,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(858,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(2901,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)],[858]) ).

thf(1076,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(3313,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)],[1076]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).

thf(1954,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).

thf(2844,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

thf(1354,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)],[75]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).

thf(2146,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).

thf(1507,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(589,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

thf(2360,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)],[589]) ).

thf(1053,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(3276,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)],[1053]) ).

thf(694,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

thf(2575,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(1114,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).

thf(3370,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(958,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(3103,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)],[958]) ).

thf(765,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(2723,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

thf(2972,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(1073,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(3308,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

thf(1645,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)],[226]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

thf(1724,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

thf(1366,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).

thf(1803,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

thf(2405,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)],[612]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

thf(2216,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1027,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).

thf(3236,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(786,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(2763,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)],[786]) ).

thf(656,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(2491,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(1243,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(901,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).

thf(2985,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)],[901]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

thf(2227,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)],[521]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

thf(1391,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).

thf(1576,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)],[191]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).

thf(1601,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1057,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(3281,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)],[1057]) ).

thf(609,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(2400,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

thf(2825,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

thf(1967,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

thf(1904,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(1518,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)],[160]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(1265,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)],[35]) ).

thf(257,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

thf(1703,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)],[257]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).

thf(1628,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)],[217]) ).

thf(260,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(1709,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)],[260]) ).

thf(573,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(2328,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).

thf(2039,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

thf(2667,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(782,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

thf(2755,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)],[782]) ).

thf(759,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).

thf(2708,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(661,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

thf(2501,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)],[661]) ).

thf(980,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(3148,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(544,axiom,
    tc_nat @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(2274,plain,
    tc_nat @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

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

thf(1313,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)],[55]) ).

thf(952,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

thf(3089,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)],[952]) ).

thf(1103,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

thf(3353,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

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

thf(1462,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(692,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

thf(2571,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)],[692]) ).

thf(756,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

thf(2703,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(1035,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(3248,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)],[1035]) ).

thf(1010,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).

thf(3204,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)],[1010]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

thf(3195,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(923,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

thf(3029,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(1151,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(3425,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)],[1151]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

thf(1430,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)],[115]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

thf(2735,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

thf(2814,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(398,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(1985,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)],[398]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

thf(3131,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)],[972]) ).

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

thf(1298,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)],[47]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

thf(2339,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)],[579]) ).

thf(931,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(3046,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(969,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

thf(3125,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

thf(1826,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)],[319]) ).

thf(1141,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(3410,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(500,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

thf(2185,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)],[500]) ).

thf(1056,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

thf(3280,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(322,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).

thf(1832,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(856,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(2897,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(1191,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)],[10]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

thf(2420,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)],[619]) ).

thf(956,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

thf(3099,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).

thf(1890,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

thf(2373,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)],[596]) ).

thf(1016,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

thf(3216,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)],[1016]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

thf(1741,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(872,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

thf(2929,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)],[872]) ).

thf(186,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(1568,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)],[186]) ).

thf(769,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).

thf(2730,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

thf(2158,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(292,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1773,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)],[292]) ).

thf(832,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(2852,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)],[832]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

thf(2388,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(1047,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(3268,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(820,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

thf(2829,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).

thf(1922,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)],[366]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).

thf(2691,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

thf(1892,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(89,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(1379,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).

thf(2403,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

thf(1514,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)],[158]) ).

thf(28,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(1247,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)],[28]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

thf(2049,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

thf(2301,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)],[559]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

thf(1815,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(903,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(2989,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(79,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(1362,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

thf(2007,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(1082,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(3322,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)],[1082]) ).

thf(1154,axiom,
    tc_IntDef_Oint @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(3431,plain,
    tc_IntDef_Oint @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(1007,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).

thf(3199,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)],[1007]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(2090,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

thf(1373,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(1067,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(3295,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)],[1067]) ).

thf(730,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(2650,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)],[730]) ).

thf(245,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

thf(1682,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)],[245]) ).

thf(577,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(2335,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).

thf(2777,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

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

thf(1283,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)],[40]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).

thf(2017,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)],[415]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

thf(1489,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)],[145]) ).

thf(883,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).

thf(2950,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

thf(1302,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(802,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).

thf(2794,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).

thf(2324,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(262,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

thf(1714,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

thf(2027,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

thf(2105,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)],[459]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

thf(1811,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)],[311]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

thf(1450,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(219,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(1632,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)],[219]) ).

thf(645,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(2469,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)],[645]) ).

thf(636,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

thf(2451,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)],[636]) ).

thf(525,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).

thf(2236,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)],[525]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

thf(1828,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)],[320]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

thf(2925,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

thf(2291,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).

thf(1383,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(1106,axiom,
    tc_IntDef_Oint @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(3357,plain,
    tc_IntDef_Oint @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(534,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

thf(2254,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(242,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

thf(1677,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)],[242]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

thf(2540,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)],[677]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

thf(1960,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)],[385]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(2555,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(436,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(2058,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)],[436]) ).

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/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

thf(2483,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(348,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(672,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

thf(2530,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(985,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).

thf(3157,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

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

thf(1351,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(807,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

thf(2804,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)],[807]) ).

thf(254,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

thf(1697,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)],[254]) ).

thf(1119,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(3378,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(664,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(2508,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)],[664]) ).

thf(890,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).

thf(2964,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).

thf(2367,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)],[593]) ).

thf(628,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(2437,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)],[628]) ).

thf(369,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).

thf(1928,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)],[369]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

thf(3068,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

thf(1377,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)],[88]) ).

thf(822,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(2833,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)],[822]) ).

thf(1002,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

thf(3189,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

thf(2861,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(1215,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)],[17]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

thf(1896,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)],[353]) ).

thf(1149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(3421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
      | ~ ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(214,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(1622,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)],[214]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).

thf(2424,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).

thf(2371,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

thf(1526,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(476,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(2137,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)],[476]) ).

thf(1109,axiom,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(3361,plain,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(2002,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(1032,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(3243,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)],[1032]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

thf(2242,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)],[528]) ).

thf(551,axiom,
    tc_nat @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(2286,plain,
    tc_nat @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(1086,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(3327,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

thf(1433,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)],[117]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).

thf(2103,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(102,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(1405,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1021,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

thf(3226,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

thf(1943,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)],[376]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).

thf(2392,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)],[605]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

thf(2154,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)],[485]) ).

thf(764,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(2718,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)],[764]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

thf(2205,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)],[510]) ).

thf(699,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(2586,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)],[699]) ).

thf(899,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

thf(2982,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)],[899]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

thf(1975,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

thf(1564,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)],[184]) ).

thf(1166,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(3450,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)],[1166]) ).

thf(509,axiom,
    tc_nat @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(2204,plain,
    tc_nat @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

thf(2473,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(120,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

thf(1438,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)],[120]) ).

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

thf(1306,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

thf(2118,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

thf(1863,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)],[337]) ).

thf(1157,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(3435,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

thf(2954,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)],[885]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

thf(1651,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(982,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

thf(3151,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

thf(2011,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1045,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(3265,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)],[1045]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).

thf(2646,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(591,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(2364,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

thf(2164,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(1079,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).

thf(3318,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).

thf(1783,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)],[297]) ).

thf(772,axiom,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(2737,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(2232,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(562,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(2307,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)],[562]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

thf(2083,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)],[448]) ).

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

thf(1736,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(860,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(2905,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

thf(1868,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)],[339]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).

thf(2773,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).

thf(2000,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

thf(1636,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(270,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

thf(1730,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(927,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

thf(3037,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)],[927]) ).

thf(705,axiom,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(2601,plain,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(532,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(2249,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)],[532]) ).

thf(704,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/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(2596,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)],[704]) ).

thf(31,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(1255,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)],[31]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

thf(2133,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)],[474]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

thf(1751,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

thf(1487,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)],[144]) ).

thf(708,axiom,
    tc_nat @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(2606,plain,
    tc_nat @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(671,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(2528,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)],[671]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

thf(2396,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)],[607]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

thf(2441,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(741,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

thf(2673,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(757,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(2705,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)],[757]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

thf(2264,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(614,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

thf(2409,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)],[614]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

thf(1387,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(355,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

thf(1900,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)],[355]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

thf(1580,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(546,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(2277,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(1025,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(3233,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)],[1025]) ).

thf(1115,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(3371,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)],[1115]) ).

thf(876,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).

thf(2937,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(318,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

thf(1824,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

thf(2150,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(852,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

thf(2890,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)],[852]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

thf(2414,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(1036,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(3250,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(25,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(1238,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)],[25]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

thf(2015,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)],[414]) ).

thf(1060,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).

thf(3286,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

thf(1560,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)],[182]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

thf(2958,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(1048,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(3269,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)],[1048]) ).

thf(719,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).

thf(2628,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).

thf(1920,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).

thf(2872,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).

thf(1296,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)],[46]) ).

thf(248,axiom,
    tc_nat @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(1687,plain,
    tc_nat @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

thf(2200,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)],[507]) ).

thf(497,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).

thf(2179,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(514,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(2213,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)],[514]) ).

thf(513,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(2211,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)],[513]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(2313,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

thf(1634,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)],[220]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

thf(2112,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

thf(1573,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(731,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

thf(2653,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(1049,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(3271,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)],[1049]) ).

thf(990,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).

thf(3166,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(632,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(2445,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(3191,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(642,axiom,
    ! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(2464,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)],[642]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

thf(2433,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)],[626]) ).

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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(2477,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(1136,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(3403,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)],[1136]) ).

thf(689,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

thf(2565,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)],[689]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).

thf(2663,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(815,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(2820,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(1069,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(3297,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)],[1069]) ).

thf(975,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(3137,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)],[975]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).

thf(2068,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).

thf(1819,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(215,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__join )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

thf(1624,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)],[215]) ).

thf(324,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

thf(1836,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)],[324]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).

thf(1787,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

thf(2181,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(922,axiom,
    tc_nat @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(3028,plain,
    tc_nat @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(582,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

thf(2345,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(925,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

thf(3033,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

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

thf(3408,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).

thf(1910,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).

thf(1983,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)],[397]) ).

thf(826,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

thf(2840,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)],[826]) ).

thf(881,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

thf(2946,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

thf(2377,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(747,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

thf(2685,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

thf(2895,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)],[855]) ).

thf(87,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(1375,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)],[87]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

thf(2577,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(21,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(1227,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)],[21]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

thf(1540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(835,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(2858,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)],[835]) ).

thf(966,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

thf(3119,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)],[966]) ).

thf(948,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

thf(3078,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

thf(2638,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)],[724]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

thf(1360,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(72,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(1350,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)],[72]) ).

thf(959,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(3105,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(1592,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(666,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

thf(2515,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(457,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(2100,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)],[457]) ).

thf(1143,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(3413,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1017,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

thf(3218,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)],[1017]) ).

thf(334,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(1856,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(344,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

thf(1878,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)],[344]) ).

thf(1124,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(3386,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(767,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

thf(2726,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(1028,axiom,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(3237,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(283,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(1755,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(541,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).

thf(2268,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(1160,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(3440,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)],[1160]) ).

thf(939,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).

thf(3060,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(995,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(3176,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(951,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

thf(3087,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)],[951]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

thf(1397,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(63,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(1329,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)],[63]) ).

thf(978,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

thf(3143,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)],[978]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

thf(1292,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)],[44]) ).

thf(6,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(1182,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)],[6]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

thf(1739,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)],[275]) ).

thf(841,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

thf(2868,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(447,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(2080,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)],[447]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

thf(1584,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)],[195]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

thf(2349,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).

thf(1446,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

thf(1493,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)],[147]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

thf(2798,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)],[804]) ).

thf(977,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(3141,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)],[977]) ).

thf(1075,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(3311,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)],[1075]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).

thf(2023,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)],[418]) ).

thf(1085,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(3326,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(387,axiom,
    tc_nat @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(1964,plain,
    tc_nat @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

thf(1659,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)],[233]) ).

thf(909,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

thf(3000,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(997,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

thf(3179,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(1138,axiom,
    tc_IntDef_Oint @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(3407,plain,
    tc_IntDef_Oint @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(687,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

thf(2561,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)],[687]) ).

thf(1013,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).

thf(3210,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)],[1013]) ).

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

thf(1424,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(638,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

thf(2455,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

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

thf(1414,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(527,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(2240,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)],[527]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).

thf(1842,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)],[327]) ).

thf(711,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(2613,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)],[711]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

thf(1937,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)],[373]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

thf(1791,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)],[301]) ).

thf(494,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

thf(2172,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(682,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).

thf(2551,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).

thf(2085,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)],[449]) ).

thf(349,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(1889,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(225,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(1644,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(209,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(1612,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)],[209]) ).

thf(897,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

thf(2978,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)],[897]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(2317,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(1066,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(3294,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

thf(2781,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(109,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(1419,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)],[109]) ).

thf(1031,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(3242,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)],[1031]) ).

thf(892,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(2968,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)],[892]) ).

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

thf(2487,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(1104,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(3354,plain,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).

thf(1552,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(305,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

thf(1799,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(378,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(1947,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(332,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(1852,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)],[332]) ).

thf(1140,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).

thf(3409,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(1090,axiom,
    tc_IntDef_Oint @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(3333,plain,
    tc_IntDef_Oint @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(543,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

thf(2272,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)],[543]) ).

thf(470,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

thf(2125,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)],[470]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

thf(1588,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)],[197]) ).

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

thf(1478,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)],[140]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).

thf(2519,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

thf(2536,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(745,axiom,
    ! [A: $i] :
      ( ( A @ class_Numeral_Onumber )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

thf(2681,plain,
    ! [A: $i] :
      ( ( A @ class_Numeral_Onumber )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

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

thf(1530,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(171,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(1539,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(824,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

thf(2836,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

thf(1456,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)],[129]) ).

thf(587,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(2355,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

thf(1932,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)],[371]) ).

thf(697,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(2581,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)],[697]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).

thf(2465,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)],[643]) ).

thf(663,axiom,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(2505,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(1127,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(3390,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)],[1127]) ).

thf(1019,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

thf(3222,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(409,axiom,
    tc_nat @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(2006,plain,
    tc_nat @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(659,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).

thf(2497,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

thf(1874,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)],[342]) ).

thf(964,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(3115,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(787,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/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(2766,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)],[787]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(2052,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)],[433]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

thf(1599,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

thf(2697,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(941,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

thf(3064,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).

thf(1720,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(961,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(3109,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)],[961]) ).

thf(395,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

thf(1979,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(946,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

thf(3074,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

thf(3005,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(988,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/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(3162,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)],[988]) ).

thf(1008,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(3201,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)],[1008]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

thf(1759,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).

thf(1393,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)],[96]) ).

thf(1168,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(3454,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).

thf(1333,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)],[65]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).

thf(1779,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

thf(1695,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)],[253]) ).

thf(849,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).

thf(2883,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oidom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).

thf(1286,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(1466,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(865,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

thf(2915,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)],[865]) ).

thf(518,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).

thf(2221,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

thf(2617,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)],[713]) ).

thf(7,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1185,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

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

thf(1732,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

thf(2909,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)],[862]) ).

thf(722,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

thf(2634,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)],[722]) ).

thf(779,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

thf(2749,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)],[779]) ).

thf(401,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).

thf(1991,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)],[401]) ).

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

thf(1318,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(680,axiom,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(2546,plain,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(785,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(2761,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)],[785]) ).

thf(428,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

thf(2043,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)],[428]) ).

thf(1055,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(3279,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(999,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).

thf(3183,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

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

thf(1712,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(329,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

thf(1846,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).

thf(2076,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)],[445]) ).

thf(778,axiom,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(2748,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(801,axiom,
    tc_nat @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(2793,plain,
    tc_nat @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

thf(1663,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)],[235]) ).

thf(451,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(2089,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

thf(2189,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__ring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

thf(1616,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)],[211]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

thf(2995,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)],[906]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).

thf(2121,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(156,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(1510,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)],[156]) ).

thf(244,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).

thf(1680,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(1041,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(3257,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(142,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

thf(1483,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)],[142]) ).

thf(37,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/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(1273,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)],[37]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

thf(1747,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)],[279]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

thf(1548,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(1043,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(3262,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1063,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(3289,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)],[1063]) ).

thf(706,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).

thf(2602,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).

thf(1595,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)],[201]) ).

thf(854,axiom,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(2894,plain,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(39,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(1278,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)],[39]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(1906,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

thf(2677,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)],[743]) ).

thf(496,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(2176,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)],[496]) ).

thf(1107,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(3358,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)],[1107]) ).

thf(545,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

thf(2275,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)],[545]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).

thf(2033,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)],[423]) ).

thf(962,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

thf(3111,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(1052,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(3274,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)],[1052]) ).

thf(1096,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(3343,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

thf(2260,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)],[537]) ).

thf(1116,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(3372,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(944,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

thf(3070,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(363,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

thf(1916,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(836,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(2859,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)],[836]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).

thf(2789,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(733,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

thf(2657,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(1058,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(3283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(1050,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

thf(3272,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

thf(1403,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

thf(2716,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(1965,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)],[388]) ).

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

thf(1520,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).

thf(2695,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(819,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(2827,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(1125,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(3387,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(1001,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).

thf(3187,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(2970,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(1080,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(3319,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

thf(2225,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)],[520]) ).

thf(347,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(1884,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)],[347]) ).

thf(94,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(1389,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)],[94]) ).

thf(1039,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(3255,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).

thf(2791,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(1030,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(3240,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

thf(1620,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(655,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

thf(2489,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(169,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).

thf(1535,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)],[169]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

thf(2806,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

thf(2991,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)],[904]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

thf(1795,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).

thf(1701,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)],[256]) ).

thf(608,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).

thf(2398,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

thf(1428,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

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

thf(1503,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)],[152]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

thf(1371,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(54,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(1312,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(773,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

thf(2738,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

thf(3123,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)],[968]) ).

thf(758,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

thf(2706,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)],[758]) ).

thf(1145,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(3416,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(1071,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/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(3302,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)],[1071]) ).

thf(992,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

thf(3170,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)],[992]) ).

thf(241,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

thf(1675,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)],[241]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

thf(2193,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)],[504]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

thf(3023,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)],[919]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).

thf(1669,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).

thf(2029,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

thf(2326,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)],[572]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

thf(1707,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)],[259]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

thf(2293,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)],[555]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

thf(3051,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(1012,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

thf(3208,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)],[1012]) ).

thf(338,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(1865,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)],[338]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

thf(2935,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(910,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(3002,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(1094,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

thf(3340,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(1997,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(784,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).

thf(2759,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(781,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(2753,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)],[781]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).

thf(2166,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(288,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(1765,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)],[288]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

thf(2457,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)],[639]) ).

thf(685,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).

thf(2557,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(953,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(3091,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)],[953]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).

thf(1464,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

thf(1638,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)],[222]) ).

thf(1105,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(3355,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(1224,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)],[20]) ).

thf(588,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

thf(2358,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)],[588]) ).

thf(568,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

thf(2319,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(1356,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(2573,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)],[693]) ).

thf(482,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(2148,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(665,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(2510,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_IntDef_Oint )
       != ( B @ c_IntDef_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

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

thf(1194,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)],[11]) ).

thf(564,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

thf(2311,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(1102,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(3352,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).

thf(2679,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(1037,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(3251,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)],[1037]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

thf(2422,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(1147,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(3419,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)],[1147]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

thf(2284,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

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

thf(1542,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

thf(2116,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

thf(1771,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(1123,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(3384,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(4,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(1175,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)],[4]) ).

thf(957,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

thf(3101,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(669,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(2521,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(676,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

thf(2538,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

thf(1408,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(2642,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(984,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

thf(3155,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)],[984]) ).

thf(522,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(2229,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)],[522]) ).

thf(1029,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(3238,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)],[1029]) ).

thf(601,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(2383,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(717,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).

thf(2624,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(902,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).

thf(2987,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

thf(1894,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)],[352]) ).

thf(657,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(2493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(1061,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(3287,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(1524,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(530,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(2246,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)],[530]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

thf(1603,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(558,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

thf(2299,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

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

thf(1722,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(739,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

thf(2669,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(1006,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

thf(3197,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)],[1006]) ).

thf(306,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(1801,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)],[306]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).

thf(2856,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(806,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

thf(2802,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)],[806]) ).

thf(250,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

thf(1690,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(942,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

thf(3066,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

thf(1969,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(987,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

thf(3160,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

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

thf(1471,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

thf(2742,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)],[775]) ).

thf(462,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(2111,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(316,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(1821,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).

thf(2785,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).

thf(2874,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).

thf(1344,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

thf(2252,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)],[533]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

thf(1381,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

thf(1688,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1170,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(3456,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)],[1170]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(1667,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

thf(2025,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)],[419]) ).

thf(811,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).

thf(2812,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(2632,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(973,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(3133,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)],[973]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(3055,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

thf(2129,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

thf(2343,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(1630,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(402,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(1993,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)],[402]) ).

thf(633,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(2446,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

thf(2757,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(869,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__ring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

thf(2923,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)],[869]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

thf(1838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

thf(1325,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).

thf(1556,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(678,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

thf(2542,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).

thf(1460,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(553,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(2289,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)],[553]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).

thf(2278,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)],[547]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

thf(2553,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(2461,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(895,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

thf(2974,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

thf(2329,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(827,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

thf(2842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(381,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(760,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).

thf(2710,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

thf(2911,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(1,negated_conjecture,
    tc_IntDef_Oint @ ( v_b @ ( v_a @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1171,plain,
    tc_IntDef_Oint @ ( v_b @ ( v_a @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

thf(2439,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)],[629]) ).

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

thf(1474,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(16,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(1213,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)],[16]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(2139,plain,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

thf(2931,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(1111,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(3363,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)],[1111]) ).

thf(1084,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(3325,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)],[1084]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

thf(2303,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)],[560]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

thf(2207,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)],[511]) ).

thf(789,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(2770,plain,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(618,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

thf(2418,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(368,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

thf(1926,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)],[368]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).

thf(2962,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(592,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

thf(2365,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(766,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(2725,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

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

thf(1699,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

thf(2401,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)],[610]) ).

thf(200,axiom,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(1594,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(432,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(2051,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1150,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(3423,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)],[1150]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).

thf(2481,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(165,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).

thf(1528,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(715,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(2620,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)],[715]) ).

thf(986,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(3159,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

thf(2064,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)],[439]) ).

thf(594,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

thf(2369,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)],[594]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).

thf(2244,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

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

thf(1435,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)],[118]) ).

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

thf(1775,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)],[293]) ).

thf(702,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

thf(2592,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)],[702]) ).

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

thf(1726,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

thf(1364,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)],[81]) ).

thf(604,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/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(2390,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)],[604]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(1250,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)],[29]) ).

thf(908,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(2999,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(1100,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(3348,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)],[1100]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

thf(2156,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)],[486]) ).

thf(252,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(1694,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(751,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

thf(2693,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)],[751]) ).

thf(900,axiom,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(2984,plain,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

thf(1973,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)],[392]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

thf(1805,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)],[308]) ).

thf(1121,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(3380,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)],[1121]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

thf(1626,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1162,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(3444,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)],[1162]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).

thf(2096,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

thf(2107,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)],[460]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(1208,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)],[15]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(2665,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)],[737]) ).

thf(1011,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

thf(3206,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)],[1011]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).

thf(2037,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(524,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).

thf(2234,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(871,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

thf(2927,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

thf(2202,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)],[508]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

thf(1340,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(1169,axiom,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

thf(3455,plain,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

thf(2054,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).

thf(1948,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(924,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

thf(3031,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)],[924]) ).

thf(813,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

thf(2816,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)],[813]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

thf(1809,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(884,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

thf(2952,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)],[884]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).

thf(1304,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1004,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(3193,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(1152,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(3427,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)],[1152]) ).

thf(1065,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(3293,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(646,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

thf(2471,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(846,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

thf(2878,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(662,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

thf(2503,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(246,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).

thf(1684,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(635,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

thf(2449,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)],[635]) ).

thf(155,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1509,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(2333,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(829,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).

thf(2846,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)],[829]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

thf(2256,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(1054,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(3278,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(384,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

thf(1958,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)],[384]) ).

thf(1064,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(3292,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(857,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).

thf(2899,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)],[857]) ).

thf(879,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

thf(2942,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)],[879]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

thf(2567,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)],[690]) ).

thf(1118,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(3376,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)],[1118]) ).

thf(735,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

thf(2661,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).

thf(2375,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1015,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

thf(3214,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)],[1015]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

thf(1647,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)],[227]) ).

thf(971,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

thf(3129,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(816,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

thf(2821,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)],[816]) ).

thf(167,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(1531,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)],[167]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

thf(2888,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

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

thf(1516,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(838,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2863,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(1077,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(3315,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)],[1077]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

thf(2060,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

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

thf(1743,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

thf(1566,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)],[185]) ).

thf(479,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(2143,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)],[479]) ).

thf(206,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).

thf(1605,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(1042,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(3260,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)],[1042]) ).

thf(700,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(2588,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)],[700]) ).

thf(770,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(2732,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)],[770]) ).

thf(375,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).

thf(1941,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(83,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

thf(1368,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(1022,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(3228,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)],[1022]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

thf(1753,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)],[282]) ).

thf(613,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).

thf(2407,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(938,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(3058,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)],[938]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(1230,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)],[22]) ).

thf(831,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).

thf(2850,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).

thf(2160,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(821,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

thf(2831,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)],[821]) ).

thf(749,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

thf(2689,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)],[749]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).

thf(2092,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(1097,axiom,
    tc_IntDef_Oint @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(3344,plain,
    tc_IntDef_Oint @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).

thf(1785,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(1262,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(578,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(2337,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)],[578]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

thf(2219,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)],[517]) ).

thf(570,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

thf(2322,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)],[570]) ).

thf(243,axiom,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(1679,plain,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(917,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

thf(3019,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(949,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(3080,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)],[949]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).

thf(1499,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(691,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).

thf(2569,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(1034,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(3246,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(399,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(1987,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)],[399]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

thf(1716,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)],[263]) ).

thf(1072,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(3305,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)],[1072]) ).

thf(116,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(1432,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)],[116]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

thf(1813,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)],[312]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

thf(1300,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

thf(1452,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(1051,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(3273,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(1091,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(3334,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)],[1091]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(1188,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)],[9]) ).

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

thf(1186,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(921,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).

thf(3026,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(624,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).

thf(2429,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(57,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(1317,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).

thf(1830,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).

thf(1763,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(970,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).

thf(3127,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(755,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

thf(2701,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(859,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(2903,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)],[859]) ).

thf(1088,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(3329,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)],[1088]) ).

thf(994,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

thf(3174,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)],[994]) ).

thf(274,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(1738,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(1218,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)],[18]) ).

thf(929,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(3041,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)],[929]) ).

thf(615,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(2411,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)],[615]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

thf(3107,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(354,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

thf(1898,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(825,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

thf(2838,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

thf(2379,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(1221,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)],[19]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(2579,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(1126,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(3388,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).

thf(1797,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

thf(3117,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(768,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

thf(2728,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(877,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(2939,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

thf(2848,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)],[830]) ).

thf(1062,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(3288,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(742,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(2675,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)],[742]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).

thf(2056,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)],[435]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).

thf(1358,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(531,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

thf(2247,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(1934,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(882,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(2948,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(622,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(2426,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(396,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

thf(1981,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)],[396]) ).

thf(74,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(1353,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(480,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(2145,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

thf(1485,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)],[143]) ).

thf(569,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

thf(2320,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

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

thf(1749,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(1020,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).

thf(3224,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(1040,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(3256,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)],[1040]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

thf(2892,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)],[853]) ).

thf(913,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
       != ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(3007,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)],[913]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).

thf(2266,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(698,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).

thf(2584,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)],[698]) ).

thf(1131,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(3398,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(991,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

thf(3168,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)],[991]) ).

thf(627,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(2435,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)],[627]) ).

thf(1156,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(3433,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)],[1156]) ).

thf(976,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

thf(3139,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)],[976]) ).

thf(1167,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(3452,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

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

thf(2479,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(1134,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(3401,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(429,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

thf(2045,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(850,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(2885,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)],[850]) ).

thf(842,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

thf(2870,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)],[842]) ).

thf(1164,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(3447,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)],[1164]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).

thf(1844,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(792,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(2775,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)],[792]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Olordered__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

thf(3039,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)],[928]) ).

thf(110,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(1421,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

thf(2013,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)],[413]) ).

thf(1133,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

thf(3400,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

thf(2626,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)],[718]) ).

thf(364,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).

thf(1918,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).

thf(1649,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(814,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

thf(2818,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)],[814]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(1180,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).

thf(1817,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(888,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(2960,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)],[888]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

thf(2078,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)],[446]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

thf(1834,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)],[323]) ).

thf(583,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(2347,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)],[583]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

thf(1412,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

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

thf(1781,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)],[296]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).

thf(2209,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

thf(2997,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)],[907]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).

thf(1448,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).

thf(2187,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oring )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(1081,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(3320,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)],[1081]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).

thf(2305,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(867,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(2919,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)],[867]) ).

thf(190,axiom,
    tc_nat @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(1575,plain,
    tc_nat @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(272,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

thf(1734,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)],[272]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

thf(1807,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)],[309]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

thf(2907,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)],[861]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).

thf(2443,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(30,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(1253,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)],[30]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

thf(2098,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

thf(2135,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)],[475]) ).

thf(673,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).

thf(2532,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)],[673]) ).

thf(1092,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(3336,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)],[1092]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

thf(2004,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)],[408]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(1745,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

thf(1854,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(701,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(2591,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(198,axiom,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(1590,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(1385,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(703,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(2594,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

thf(2174,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)],[495]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

thf(1476,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

thf(1481,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)],[141]) ).

thf(1122,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

thf(3383,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(817,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(2823,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(1018,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).

thf(3220,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(1026,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(3235,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

thf(2431,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)],[625]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

thf(3003,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)],[911]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

thf(1822,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)],[317]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

thf(2526,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(617,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).

thf(2416,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).

thf(1558,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(484,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

thf(2152,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)],[484]) ).

thf(538,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

thf(2262,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

thf(2394,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(3085,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

thf(2944,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)],[880]) ).

thf(1083,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

thf(3324,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

thf(2796,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

thf(2041,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)],[427]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

thf(2066,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)],[440]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

thf(2183,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)],[499]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(1607,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)],[207]) ).

thf(1101,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(3351,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

thf(1661,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(467,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(2120,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)],[467]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).

thf(2315,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)],[566]) ).

thf(866,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

thf(2917,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).

thf(2009,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

thf(1861,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)],[336]) ).

thf(886,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

thf(2956,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)],[886]) ).

thf(146,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(1491,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)],[146]) ).

thf(998,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

thf(3181,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(648,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(2475,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(729,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

thf(2648,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(1153,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

thf(3430,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

thf(1777,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)],[294]) ).

thf(1046,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

thf(3267,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).

thf(1294,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(1440,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)],[121]) ).

thf(981,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

thf(3149,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)],[981]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).

thf(1308,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

thf(2198,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(590,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(2362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

thf(2162,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

thf(1444,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)],[123]) ).

thf(122,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(1442,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)],[122]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

thf(2779,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(416,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

thf(2019,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(1148,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(3420,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).

thf(1614,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

thf(1348,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).

thf(2287,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

thf(1642,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).

thf(1512,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)],[157]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).

thf(1578,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(602,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(2385,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)],[602]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

thf(1546,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(1395,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(1044,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(3264,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(343,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).

thf(1876,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ominus )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(240,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

thf(1673,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)],[240]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

thf(1757,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)],[284]) ).

thf(788,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

thf(2768,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)],[788]) ).

thf(989,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).

thf(3164,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)],[989]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

thf(1908,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)],[359]) ).

thf(1120,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(3379,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

thf(2123,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(516,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(2218,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(536,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

thf(2258,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)],[536]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).

thf(2517,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).

thf(2683,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(674,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

thf(2534,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(1024,axiom,
    ! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(3232,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)],[1024]) ).

thf(1117,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).

thf(3373,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(707,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).

thf(2604,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(1009,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(3203,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(940,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

thf(3062,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(915,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).

thf(3015,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)],[915]) ).

thf(1087,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(3328,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

thf(1989,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(80,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(1363,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)],[80]) ).

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

thf(1495,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(232,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

thf(1657,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)],[232]) ).

thf(1099,axiom,
    tc_IntDef_Oint @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(3347,plain,
    tc_IntDef_Oint @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(996,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

thf(3177,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)],[996]) ).

thf(777,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

thf(2746,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

thf(1789,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(864,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).

thf(2913,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(762,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).

thf(2714,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(714,axiom,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(2619,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(796,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(2783,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(681,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

thf(2549,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)],[681]) ).

thf(1074,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(3309,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(979,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(3145,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(723,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

thf(2636,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)],[723]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).

thf(1436,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(335,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

thf(1859,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)],[335]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

thf(2751,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(805,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

thf(2800,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(66,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(1335,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)],[66]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__group__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

thf(2070,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)],[442]) ).

thf(2,negated_conjecture,
    tc_IntDef_Oint @ ( v_c @ ( v_b @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1172,plain,
    tc_IntDef_Oint @ ( v_c @ ( v_b @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(1410,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(1288,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(12,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(1197,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)],[12]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

thf(2223,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(137,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(1473,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).

thf(2021,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__group__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

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

thf(1346,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)],[70]) ).

thf(208,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

thf(1610,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(394,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/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(1977,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)],[394]) ).

thf(920,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(3025,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(937,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(3057,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(1108,axiom,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(3360,plain,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).

thf(1582,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(644,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

thf(2467,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

thf(1550,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)],[177]) ).

thf(1033,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

thf(3245,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(1128,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(3392,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)],[1128]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

thf(2699,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)],[754]) ).

thf(1095,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(3341,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)],[1095]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

thf(1930,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)],[370]) ).

thf(586,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).

thf(2353,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(24,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(1236,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)],[24]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

thf(2127,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)],[471]) ).

thf(1110,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(3362,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).

thf(2810,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(891,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

thf(2966,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)],[891]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(1268,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)],[36]) ).

thf(1142,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(3411,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)],[1142]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

thf(2485,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

thf(1537,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(202,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).

thf(1597,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)],[202]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).

thf(2687,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(839,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(2864,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(1880,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(947,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

thf(3076,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)],[947]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

thf(3113,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(356,axiom,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(1902,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(1129,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(3394,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)],[1129]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

thf(1505,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

thf(1399,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(542,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(2270,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)],[542]) ).

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

thf(1331,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(3437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_less ) ) )
      | ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

thf(1320,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

thf(1653,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

thf(1962,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)],[386]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

thf(3096,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

thf(2866,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)],[840]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

thf(1848,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)],[330]) ).

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

thf(3432,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).

thf(2453,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Numeral_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

thf(2087,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(932,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

thf(3047,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)],[932]) ).

thf(1068,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).

thf(3296,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(732,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

thf(2655,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)],[732]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

thf(2879,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)],[847]) ).

thf(725,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

thf(2640,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)],[725]) ).

thf(688,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).

thf(2563,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).

thf(2881,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).

thf(1945,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(1014,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

thf(3212,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(1070,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(3299,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)],[1070]) ).

thf(1137,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(3405,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)],[1137]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

thf(2074,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)],[444]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

thf(2238,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)],[526]) ).

thf(557,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).

thf(2297,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(1161,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

thf(3443,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(712,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

thf(2615,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)],[712]) ).

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

thf(1769,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)],[290]) ).

thf(585,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

thf(2351,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

thf(2170,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)],[493]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

thf(2834,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(905,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

thf(2993,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

thf(2191,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)],[503]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

thf(1912,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)],[361]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Opordered__semiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(2980,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)],[898]) ).

thf(926,axiom,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

thf(3035,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)],[926]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

thf(1417,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)],[108]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(1870,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)],[340]) ).

thf(790,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(2771,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)],[790]) ).

thf(3810,plain,
    $false,
    inference(e,[status(thm)],[2630,1718,2094,2876,2921,3397,1840,2427,2544,2331,1686,3021,1322,1665,1586,1501,2612,1469,2744,1369,2295,3053,3345,2341,2109,2131,1454,2031,2072,1767,3399,1995,1315,2787,1850,2499,2559,3449,1956,1950,2280,1554,3172,1200,3185,3317,2622,2062,3153,1401,3098,1728,2282,2114,1692,1173,2309,2976,3072,1924,2940,1406,1290,1882,2808,1522,2644,2495,3230,2381,2659,3417,1618,3285,1422,1569,1939,2671,1544,3012,1205,1971,1793,3402,2854,1533,1426,1671,3439,1655,3049,2607,1310,3135,3044,1233,1327,1640,1458,1497,3017,2195,1705,2035,3332,3367,3365,2740,1999,3446,2448,3338,2933,1275,2141,1872,2712,2168,1260,3253,2459,3414,1761,1342,3121,2901,3313,1954,2844,1354,2146,1507,2360,3276,2575,3370,3103,2723,2972,1914,3308,1645,1724,1366,1803,2405,2216,3236,2763,2491,1243,2985,2227,1391,1576,1601,3281,2400,2825,1967,1904,1518,1265,1703,1628,1709,2328,2039,2667,2755,2708,2501,3148,2274,1313,3089,3353,1462,2571,2703,3248,3204,3195,3029,3425,1430,2735,2814,1985,3131,1298,2339,3046,3125,1826,3410,2185,3280,1832,2897,1191,2420,3099,1890,2373,3216,1741,2929,1568,2730,2158,1773,2852,2388,3268,2829,1922,2691,1892,1379,2403,1514,1247,2049,2301,1815,2989,1362,2007,3322,3431,3199,2090,1373,3295,2650,1682,2335,2777,1283,2017,1489,2950,1302,2794,2324,1714,2027,2105,1811,1450,1632,2469,2451,2236,1828,2925,2291,1383,3357,2254,1677,2540,1960,2555,2058,2483,1886,2530,3157,1351,2804,1697,3378,2508,2964,2367,2437,1928,3068,1377,2833,3189,2861,1215,1896,3421,1622,2424,2371,1526,2137,3361,2002,3243,2242,2286,3327,1433,2103,1405,3226,1943,2392,2154,2718,2205,2586,2982,1975,1564,3450,2204,2473,1438,1306,2118,1863,3435,2954,1651,3151,2011,3265,2646,2364,2164,2047,3318,1783,2737,2232,2307,2083,1736,2905,1868,2773,2000,1636,1730,3037,2601,2249,2596,1255,2133,1751,1487,2606,2528,2396,2441,2673,2705,2264,2409,1387,1900,1580,2277,3233,3371,2937,1824,2150,2890,2414,3250,1238,2015,3286,1560,2958,3269,2628,1920,2872,1296,1687,2200,2179,2213,2211,2313,1634,2112,1573,2653,3271,3166,2445,3191,2464,2433,2477,3403,2565,2663,2820,3297,3137,2068,1819,1624,1836,1787,2181,3028,2345,3033,3408,1910,1983,2840,2946,2377,2685,2895,1375,2577,1227,1540,2858,3119,3078,2638,1360,1350,3105,1592,2515,2100,3413,3218,1856,1878,3386,2726,3237,1755,2268,3440,3060,3176,3087,1397,1329,3143,1292,1182,1739,2868,2080,1584,2349,1446,1493,2798,3141,3311,2023,3326,1964,1659,3000,3179,3407,2561,3210,1424,2455,1414,2240,1842,2613,1937,1791,2172,2551,2085,1889,1644,1612,2978,2317,3294,2781,1419,3242,2968,2487,3354,1552,1799,1947,1852,3409,3333,2272,2125,1588,1478,2519,2536,2681,1530,1539,2836,1456,2355,1932,2581,2465,2505,3390,3222,2006,2497,1874,3115,2766,2052,1599,2697,3064,1720,3109,1979,3074,3005,3162,3201,1759,1393,3454,1333,1779,1695,2883,1286,1466,2915,2221,2617,1185,1732,2909,2634,2749,1991,1318,2546,2761,2043,3279,3183,1712,1846,2076,2748,2793,1663,2089,2189,1616,2995,2121,1510,1680,3257,1483,1273,1747,1548,3262,3289,2602,1595,2894,1278,1906,2677,2176,3358,2275,2033,3111,3274,3343,2260,3372,3070,1916,2859,2789,2657,3283,3272,1403,2716,1965,1520,2695,2827,3387,3187,2970,3319,2225,1884,1389,3255,2791,3240,1620,2489,1535,2806,2991,1795,1701,2398,1428,1503,1371,1312,2738,3123,2706,3416,1258,3302,3170,1675,2193,3023,1669,2029,2326,1707,2293,3051,3208,1865,2935,3002,3340,1997,2759,2753,2166,1765,2457,2557,3091,1464,1638,3355,1224,2358,2319,1356,2573,2148,2510,1194,2311,3352,2679,3251,2422,3419,2284,1542,2116,1771,3384,1571,1175,3101,2521,2538,1408,2642,3155,2229,3238,2383,2624,2987,1894,2493,3287,1524,2246,1603,2299,1722,2669,3197,1801,2856,2802,1690,3066,1969,3160,1471,2742,2111,1821,2785,2874,1344,2252,1381,1688,3456,1667,2025,2812,2632,3133,3055,2129,2343,1630,1993,2446,2757,2923,1838,1325,1556,2542,1460,2289,2278,2553,2461,2974,2329,2842,1952,2710,2911,1171,2439,1474,1213,2139,2931,3363,3325,2303,2207,2770,2418,1926,2962,2365,2725,1699,2401,1594,2051,3423,1245,2481,1528,2620,3159,2064,2369,2244,1435,1775,2592,1726,1364,2390,1250,2999,3348,2156,1694,2693,2984,1973,1805,3380,1562,1626,3444,2096,2107,1208,2665,3206,2037,2234,2927,2202,1340,3455,2054,1948,3031,2816,1809,2952,1304,3193,3427,3293,2471,2878,2503,1684,2449,1509,2333,2846,2256,3278,1958,3292,2899,2942,2567,3376,2661,2375,3214,1647,3129,2821,1531,2888,1516,2863,3315,2060,1743,1566,2143,1605,3260,2588,2732,1941,1368,3228,1753,2407,3058,1230,2850,2160,2831,2689,2092,3344,1785,1262,2337,2219,2322,1679,3019,3080,1499,2569,3246,1987,1716,3305,1432,1813,1300,1452,3273,3334,1188,1186,3026,2429,1317,1830,1763,3127,2701,2903,3329,3174,1738,1218,3041,2411,3107,1898,2838,2379,1221,2579,3388,1797,3117,2728,2939,2848,3288,2675,2056,1358,2247,1934,2948,2426,1981,1353,2145,1485,2320,1749,3224,3256,2892,3007,2266,2584,3398,3168,2435,3433,3139,3452,2479,3401,2045,2885,2870,3447,1844,2775,3039,1421,2013,3400,2626,1918,1649,2818,1180,1817,2960,2078,1834,2347,1412,1781,2209,2997,1448,2187,3320,2305,2919,1575,1734,1807,2907,2443,1253,2098,2135,2532,3336,2004,1745,1854,2591,1590,1385,2594,2174,1476,1481,3383,2823,3220,3235,2431,3003,1822,2526,2416,1558,2152,2262,2394,3085,2944,3324,2796,2041,2066,2183,1607,3351,1661,2120,2315,2917,2009,1861,2956,1491,3181,2475,2648,3430,1777,3267,1294,1440,3149,1308,2198,2362,2162,1444,1442,2779,2019,3420,1614,1348,2287,1642,1512,1578,2385,1546,1395,3264,1876,1673,1757,2768,3164,1908,3379,2123,2218,2258,2517,2683,2534,3232,3373,2604,3203,3062,3015,3328,1989,1363,1495,1657,3347,3177,2746,1789,2913,2714,2619,2783,2549,3309,3145,2636,1436,1859,2751,2800,1335,2070,1172,1410,1288,1197,2223,1473,2021,1346,1610,1977,3025,3057,3360,1582,2467,1550,3245,3392,2699,3341,1930,2353,1236,2127,3362,2810,2966,1268,3411,2485,1537,1597,2687,2864,1880,3076,3113,1902,3394,1505,1399,2270,1331,3437,1320,1653,1962,3096,2866,1848,3432,2453,2087,3047,3296,2655,2879,2640,2563,2881,1945,3212,3299,3405,2074,2238,2297,3443,2615,1769,2351,2170,2834,2993,2191,1912,2980,3035,1417,1870,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38  % Computer : n018.cluster.edu
% 0.12/0.38  % Model    : x86_64 x86_64
% 0.12/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38  % Memory   : 8046.5625MB
% 0.12/0.38  % OS       : Linux 6.8.0-71-generic
% 0.12/0.39  % CPULimit : 300
% 0.12/0.39  % WCLimit  : 300
% 0.12/0.39  % DateTime : Sat Sep 26 08:20:38 UTC 2026
% 0.12/0.39  % CPUTime  : 
% 0.12/0.39  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.95/1.09  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.10/1.65  % [INFO] 	 Parsing done (560ms). 
% 2.10/1.66  % [INFO] 	 Running in sequential loop mode. 
% 2.75/1.87  % [INFO] 	 eprover registered as external prover. 
% 2.75/1.87  % [INFO] 	 Scanning for conjecture ... 
% 3.12/1.99  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ... 
% 4.15/2.20  % [INFO] 	 Axiom selection finished. Selected 1167 axioms (removed 190 axioms). 
% 4.96/2.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.96/2.38  % [INFO] 	 Type checking passed. 
% 4.96/2.39  % [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 ... 
% 16.73/4.82  % External prover 'e' found a proof!
% 16.73/4.82  % [INFO] 	 Killing All external provers ... 
% 16.73/4.83  % Time passed: 4286ms (effective reasoning time: 3161ms)
% 16.73/4.84  % Axioms used in derivation (1167): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Oidom_20, clsrel_Ring__and__Field_Oordered__idom_3, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Oidom_17, clsarity_IntDef__Oint_57, clsrel_OrderedGroup_Olordered__ab__group__abs_3, clsrel_Ring__and__Field_Osemiring__1__cancel_12, cls_Nat_Ole__0__eq__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, clsrel_Ring__and__Field_Opordered__comm__semiring_14, clsrel_Ring__and__Field_Opordered__ring_2, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, clsrel_Ring__and__Field_Oring__1_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, cls_IntDiv_Ozdvd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, clsarity_IntDef__Oint_4, cls_List_Ofinite__set_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, clsrel_Ring__and__Field_Ocomm__ring_3, clsrel_Ring__and__Field_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodI_0, clsrel_Ring__and__Field_Oordered__semidom_16, clsrel_OrderedGroup_Opordered__ab__group__add_6, clsarity_nat_32, clsarity_nat_26, clsrel_Numeral_Onumber__ring_1, clsrel_Ring__and__Field_Olordered__ring_8, clsrel_Ring__and__Field_Ocomm__ring_12, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Oordered__ring__strict_7, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, clsrel_Ring__and__Field_Olordered__ring_14, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsrel_Ring__and__Field_Ocomm__ring_17, cls_List_Olists_ONil_0, cls_Set_OInterD_0, clsarity_IntDef__Oint_45, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20, clsrel_Power_Orecpower_17, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7, clsrel_OrderedGroup_Olordered__ab__group_13, cls_Divides_Omod__eq__0D__dest_0, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_6, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Ring__and__Field_Oordered__idom_43, clsrel_OrderedGroup_Olordered__ab__group_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_7, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oring_13, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, clsrel_OrderedGroup_Omonoid__mult_2, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_SetInterval_OgreaterThan__iff__iff2_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, clsrel_Ring__and__Field_Oordered__idom_12, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, clsarity_nat_15, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4, cls_List_ONil__is__append__conv__iff2_0, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_10, clsrel_Ring__and__Field_Olordered__ring_3, clsrel_Power_Orecpower_14, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_Ring__and__Field_Oidom_29, clsarity_IntDef__Oint_24, clsrel_Ring__and__Field_Oidom_26, clsrel_OrderedGroup_Osemigroup__add_0, clsrel_Ring__and__Field_Oring_10, clsrel_Numeral_Onumber__ring_16, clsrel_OrderedGroup_Olordered__ab__group_9, clsrel_Power_Orecpower_6, clsarity_nat_10, clsrel_Ring__and__Field_Oordered__ring__strict_26, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_Ring__and__Field_Oidom_13, clsrel_Ring__and__Field_Opordered__ring_14, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__ring__1_1, clsrel_Ring__and__Field_Oring__1_18, clsrel_OrderedGroup_Oab__group__add_6, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, clsrel_OrderedGroup_Olordered__ab__group__abs_8, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, clsrel_Ring__and__Field_Ocomm__ring__1_16, cls_Nat_Oless__Suc0__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, clsrel_Numeral_Onumber__ring_27, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, clsrel_Ring__and__Field_Opordered__ring_19, cls_Finite__Set_OFinites_OemptyI_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, clsrel_Numeral_Onumber__ring_24, clsrel_Ring__and__Field_Oordered__semidom_23, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsrel_Power_Orecpower_5, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4, clsrel_OrderedGroup_Olordered__ab__group__abs_13, clsrel_Ring__and__Field_Ocomm__ring__1_20, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, clsrel_Ring__and__Field_Oordered__idom_48, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, clsrel_Ring__and__Field_Olordered__ring_4, clsrel_Ring__and__Field_Osemiring_1, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsrel_Ring__and__Field_Oordered__ring__strict_14, clsrel_Ring__and__Field_Oordered__idom_56, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, cls_Finite__Set_OFinites_OinsertI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, clsrel_Ring__and__Field_Oidom_10, clsarity_set_2, clsarity_nat_25, clsrel_Ring__and__Field_Oordered__idom_17, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Oring_6, clsrel_OrderedGroup_Olordered__ab__group__join_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Ring__and__Field_Oring__1_19, clsrel_OrderedGroup_Oab__group__add_5, clsrel_Ring__and__Field_Olordered__ring_1, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsrel_Ring__and__Field_Oring__1_14, cls_List_Olistrel__Nil1_0, clsrel_Numeral_Onumber__ring_12, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, clsrel_Ring__and__Field_Ocomm__ring__1_5, clsarity_IntDef__Oint_3, cls_Nat_Onot__less0__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, clsrel_Ring__and__Field_Ocomm__ring__1_13, clsrel_OrderedGroup_Olordered__ab__group__meet_9, clsarity_IntDef__Oint_60, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Numeral_Onumber__ring_23, clsrel_Numeral_Onumber__ring_20, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_Nat_Oless__one__iff1_0, clsrel_Ring__and__Field_Ocomm__ring_9, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, clsrel_Ring__and__Field_Oidom_1, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Set_OComplI_0, clsrel_OrderedGroup_Opordered__ab__group__add_8, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_Ring__and__Field_Ocomm__semiring__0_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__comm__semiring_8, clsrel_Ring__and__Field_Ocomm__ring__1_27, cls_Relation_OconverseE_1, clsrel_Ring__and__Field_Olordered__ring_21, clsrel_OrderedGroup_Oab__group__add_0, clsarity_nat_47, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_14, cls_Finite__Set_Ofinite__Int_0, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, clsrel_OrderedGroup_Opordered__ab__group__add_10, clsrel_Ring__and__Field_Oordered__idom_28, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsrel_Ring__and__Field_Oordered__semiring__strict_19, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, clsrel_Ring__and__Field_Osemiring__1_4, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, clsrel_Ring__and__Field_Oidom_21, clsarity_IntDef__Oint_49, clsrel_Ring__and__Field_Ocomm__ring_10, clsrel_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, clsrel_Ring__and__Field_Opordered__ring_6, clsarity_IntDef__Oint_38, clsrel_Ring__and__Field_Oring_1, clsrel_Ring__and__Field_Oidom_7, clsrel_Ring__and__Field_Opordered__ring_11, clsrel_OrderedGroup_Oab__semigroup__mult_0, clsrel_Ring__and__Field_Opordered__semiring_2, clsrel_Ring__and__Field_Opordered__ring_22, clsrel_Ring__and__Field_Osemiring__0_2, clsrel_Ring__and__Field_Ocomm__ring_13, cls_SetInterval_OlessThan__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_49, clsrel_Ring__and__Field_Osemiring__0_7, cls_Set_OUnCI_1, clsrel_OrderedGroup_Olordered__ab__group__meet_12, clsrel_Ring__and__Field_Oring__1_2, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14, clsarity_IntDef__Oint_16, clsrel_Ring__and__Field_Oordered__semiring__strict_3, clsrel_Ring__and__Field_Osemiring__1_10, cls_Relation_ORangeE_0, clsrel_Ring__and__Field_Oordered__semiring__strict_8, cls_Set_OInterI_1, clsrel_Numeral_Onumber__ring_19, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_OrderedGroup_Olordered__ab__group__abs_10, cls_List_Oset__empty__iff2_0, clsrel_Numeral_Onumber__ring_5, clsrel_Ring__and__Field_Ocomm__semiring__1_16, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, clsarity_nat_36, clsrel_Ring__and__Field_Olordered__ring_25, clsrel_Ring__and__Field_Ocomm__ring_0, clsarity_nat_18, clsrel_Ring__and__Field_Oordered__semidom_13, cls_Product__Type_OPair__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_Set_OinsertCI_0, clsrel_Ring__and__Field_Olordered__ring_10, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, cls_Set_OPow__iff__iff2_0, clsrel_Ring__and__Field_Oring__1_11, cls_Finite__Set_Ofinite__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Opordered__ab__group__add_11, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Power_Orecpower_13, clsrel_Ring__and__Field_Oordered__semidom_24, clsarity_IntDef__Oint_19, clsrel_Ring__and__Field_Oordered__semiring__strict_16, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5, clsrel_OrderedGroup_Olordered__ab__group_4, cls_List_Oappend__in__lists__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semiring__strict_21, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, clsrel_Ring__and__Field_Oring__1_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, clsrel_Ring__and__Field_Oidom_25, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Oordered__ring__strict_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsarity_IntDef__Oint_59, clsarity_nat_22, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, clsrel_OrderedGroup_Ocomm__monoid__mult_3, cls_Set_OCompl__subset__Compl__iff__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29, cls_Datatype__Universe_OIn0__not__In1__iff1_0, clsrel_Power_Orecpower_18, clsrel_Ring__and__Field_Oidom_6, clsrel_Ring__and__Field_Opordered__ring_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, clsarity_nat_44, clsrel_OrderedGroup_Olordered__ab__group__abs_4, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, clsrel_Ring__and__Field_Osemiring__1__cancel_4, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Oring__1_6, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Osemiring__1_3, cls_Finite__Set_Ofinite__Un__iff1_0, clsrel_Numeral_Onumber__ring_6, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Datatype__Universe_OdprodE_1, clsrel_OrderedGroup_Olordered__ab__group_6, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, cls_Set_OUNIV__I_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, clsrel_Ring__and__Field_Ocomm__semiring_2, clsrel_Numeral_Onumber__ring_28, clsarity_IntDef__Oint_58, cls_Set_OCompl__eq__Compl__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, clsrel_Ring__and__Field_Oordered__idom_38, clsrel_Ring__and__Field_Oordered__idom_2, clsrel_OrderedGroup_Olordered__ab__group__abs_5, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__semidom_3, clsrel_Ring__and__Field_Opordered__ring_3, cls_List_OlistsE_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5, cls_List_Olength__0__conv__iff2_0, clsrel_Power_Orecpower_4, cls_Divides_Odvd__0__left__iff__iff2_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0, cls_List_Oself__append__conv__iff2_0, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Olordered__ring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_11, clsarity_IntDef__Oint_53, cls_List_Owf__lex_0, cls_SetInterval_OatMost__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_36, clsarity_nat_27, cls_Relation_ODomainI_0, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, clsrel_Ring__and__Field_Ocomm__semiring_5, clsrel_Ring__and__Field_Oordered__idom_26, cls_Set_OinsertE_0, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_Ring__and__Field_Oring__1_15, clsrel_Ring__and__Field_Oordered__ring__strict_8, clsrel_Ring__and__Field_Oordered__idom_52, clsrel_Ring__and__Field_Oordered__ring__strict_25, clsrel_Ring__and__Field_Opordered__semiring_7, clsrel_Ring__and__Field_Ocomm__ring__1_0, clsarity_IntDef__Oint_64, clsrel_Ring__and__Field_Opordered__ring_13, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, clsrel_OrderedGroup_Ocomm__monoid__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_27, cls_Set_Onot__psubset__empty__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_14, clsarity_IntDef__Oint_14, clsrel_Ring__and__Field_Opordered__comm__semiring_13, clsarity_IntDef__Oint_7, cls_Set_OUnE_0, clsrel_Ring__and__Field_Oring_9, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring__1_10, clsrel_OrderedGroup_Olordered__ab__group_0, clsarity_nat_16, clsrel_Ring__and__Field_Opordered__cancel__semiring_12, cls_SetInterval_OlessThan__subset__iff__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, clsrel_OrderedGroup_Olordered__ab__group_14, clsrel_Ring__and__Field_Oidom_14, clsrel_Ring__and__Field_Ocomm__semiring__1_11, clsrel_Ring__and__Field_Oordered__idom_10, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_Ring__and__Field_Oordered__ring__strict_36, clsrel_Ring__and__Field_Osemiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__ring__strict_11, clsrel_Ring__and__Field_Ocomm__ring_16, clsrel_Ring__and__Field_Olordered__ring_19, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, clsrel_Ring__and__Field_Ocomm__ring__1_21, clsrel_Ring__and__Field_Oordered__idom_47, clsrel_Ring__and__Field_Ocomm__ring_2, clsarity_nat_38, clsrel_Ring__and__Field_Oordered__ring__strict_5, clsrel_Numeral_Onumber__ring_2, clsrel_Numeral_Onumber__ring_17, cls_Set_OComplD__dest_0, clsrel_Ring__and__Field_Ocomm__semiring__0_3, clsrel_Ring__and__Field_Oordered__semidom_8, cls_Set_OUn__empty__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12, cls_Relation_Orel__compE_2, clsrel_Ring__and__Field_Oordered__idom_15, clsrel_Ring__and__Field_Ocomm__ring__1_19, clsrel_OrderedGroup_Olordered__ab__group_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, cls_Relation_OImageE_1, cls_Set_OsingletonD__dest_0, clsrel_Ring__and__Field_Olordered__ring_7, clsarity_IntDef__Oint_20, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Ocomm__ring__1_4, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_16, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, clsrel_Ring__and__Field_Ocomm__ring__1_14, clsrel_Ring__and__Field_Oordered__idom_31, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OdiagE_0, clsrel_Ring__and__Field_Ocomm__ring__1_26, cls_SetInterval_Ofinite__atLeastAtMost_0, clsrel_Ring__and__Field_Oordered__ring__strict_21, cls_SetInterval_OatMost__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, cls_GCD_Ogcd__dvd1_0, clsrel_Ring__and__Field_Oring_5, cls_SetInterval_Ofinite__atLeastLessThan_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Olordered__ab__group__join_7, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, clsrel_Ring__and__Field_Olordered__ring_26, cls_Set_OUn__empty__iff1_0, clsrel_Ring__and__Field_Oordered__idom_22, clsrel_Power_Orecpower_10, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, clsrel_Ring__and__Field_Oordered__idom_57, clsrel_Ring__and__Field_Opordered__cancel__semiring_2, cls_Wellfounded__Recursion_Owf__insert__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_4, clsrel_Ring__and__Field_Opordered__ring_12, clsrel_Ring__and__Field_Osemiring__0_6, clsrel_Ring__and__Field_Oordered__ring__strict_4, cls_Set_Oempty__subsetI_0, clsrel_Numeral_Onumber__ring_13, clsrel_Ring__and__Field_Ocomm__ring__1_25, clsrel_OrderedGroup_Olordered__ab__group__join_13, clsrel_Ring__and__Field_Oordered__ring__strict_32, cls_Relation_OIdI_0, clsarity_IntDef__Oint_26, clsrel_Ring__and__Field_Ocomm__ring__1_15, clsarity_IntDef__Oint_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15, cls_List_Oappend__is__Nil__conv__iff2_0, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_11, clsrel_Ring__and__Field_Oordered__semidom_17, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, clsrel_Ring__and__Field_Oordered__idom_29, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, clsrel_Ring__and__Field_Oordered__ring__strict_15, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_Ring__and__Field_Osemiring__1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_14, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_11, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2, cls_Nat_Oadd__gr__0__iff2_1, clsrel_Ring__and__Field_Opordered__ring_9, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_2, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_8, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, clsrel_Ring__and__Field_Oring_2, cls_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__idom_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, clsrel_Ring__and__Field_Olordered__ring_22, clsarity_nat_37, cls_Product__Type_OPair__eq__iff1_1, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, clsrel_Ring__and__Field_Oaxclass__abs__if_1, clsrel_Ring__and__Field_Oidom_11, clsrel_Ring__and__Field_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, cls_List_Osame__append__eq__iff1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Oidom_2, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, clsrel_Ring__and__Field_Oring__1_1, cls_SetInterval_OatLeast__iff__iff2_0, cls_GCD_Ogcd__greatest__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, clsrel_OrderedGroup_Opordered__ab__group__add_2, cls_Datatype_Oelem__o2s__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__meet_11, clsrel_Ring__and__Field_Olordered__ring_11, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__0_10, clsrel_Ring__and__Field_Opordered__ring_7, cls_Relation_OconverseE_0, clsarity_IntDef__Oint_42, clsrel_OrderedGroup_Oab__group__add_4, cls_IntDiv_Ozdvd__1__left_0, cls_List_Olength__greater__0__conv__iff2_0, clsrel_Numeral_Onumber__ring_30, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__idom_39, cls_SetInterval_OatMost__subset__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_6, clsrel_Ring__and__Field_Opordered__comm__semiring_9, clsrel_Ring__and__Field_Oordered__semidom_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0, cls_GCD_Ogcd__greatest__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_11, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6, clsarity_nat_0, cls_Datatype__Universe_OuprodE_2, clsarity_nat_43, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_0, clsrel_Ring__and__Field_Osemiring__1_7, cls_Datatype__Universe_OIn1__not__In0__iff1_0, clsarity_IntDef__Oint_18, cls_List_Olist_Oinject__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_13, clsrel_Ring__and__Field_Opordered__cancel__semiring_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, clsrel_Numeral_Onumber__ring_7, clsarity_nat_34, clsrel_Ring__and__Field_Ocomm__semiring__1_10, clsrel_OrderedGroup_Olordered__ab__group_5, clsrel_Ring__and__Field_Opordered__ring_17, clsrel_OrderedGroup_Olordered__ab__group__abs_6, clsrel_OrderedGroup_Opordered__ab__semigroup__add_3, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_8, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8, clsrel_Ring__and__Field_Oordered__semidom_25, clsrel_OrderedGroup_Opordered__ab__group__add_4, clsrel_LOrder_Omeet__semilorder_0, clsrel_Ring__and__Field_Olordered__ring_18, clsrel_Power_Orecpower_3, clsarity_IntDef__Oint_29, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1, clsrel_Ring__and__Field_Osemiring__0_1, cls_GCD_Ogcd__greatest__iff__iff1_1, clsrel_Orderings_Olinorder_2, cls_Datatype__Universe_OuprodE_0, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8, clsrel_Ring__and__Field_Olordered__ring_23, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring_1, clsrel_Ring__and__Field_Oordered__idom_46, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_OrderedGroup_Olordered__ab__group__meet_10, clsrel_Ring__and__Field_Oordered__idom_19, clsarity_nat_45, cls_Set_ODiffE_0, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_Ring__and__Field_Olordered__ring_12, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsarity_nat_17, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, clsrel_Ring__and__Field_Ocomm__ring__1_2, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, clsrel_Ring__and__Field_Oidom_9, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Relation_ORangeI_0, cls_Divides_Odvd__triv__right_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__idom_14, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsrel_Ring__and__Field_Oordered__idom_20, clsrel_Ring__and__Field_Opordered__comm__semiring_12, clsrel_Ring__and__Field_Ocomm__ring_1, clsrel_OrderedGroup_Olordered__ab__group__join_11, clsrel_Ring__and__Field_Opordered__cancel__semiring_5, clsrel_Ring__and__Field_Oordered__semidom_27, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, clsrel_Ring__and__Field_Oidom_15, cls_List_Oset__empty__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, clsrel_Ring__and__Field_Oidom_24, clsrel_Ring__and__Field_Oordered__semidom_4, clsrel_Numeral_Onumber__ring_22, cls_Nat_Onot__add__less1__iff1_0, clsrel_Numeral_Onumber__ring_11, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, clsarity_IntDef__Oint_8, clsrel_Ring__and__Field_Opordered__cancel__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16, cls_Relation_Opair__in__Id__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4, clsrel_Ring__and__Field_Opordered__ring_0, clsarity_IntDef__Oint_54, clsarity_nat_28, clsrel_Ring__and__Field_Ocomm__semiring_6, cls_Set_OIntI_0, clsrel_Ring__and__Field_Ocomm__ring_8, clsrel_Ring__and__Field_Osemiring__0__cancel_6, clsarity_nat_39, cls_Finite__Set_Ofinite__Union_1, clsrel_LOrder_Ojoin__semilorder_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, clsrel_OrderedGroup_Osemigroup__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20, clsrel_Ring__and__Field_Oordered__idom_1, clsarity_nat_23, clsrel_Ring__and__Field_Oidom_22, clsrel_Ring__and__Field_Oidom_5, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, clsrel_Ring__and__Field_Opordered__semiring_8, clsrel_OrderedGroup_Oab__group__add_3, clsrel_Ring__and__Field_Oring__1_12, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Ozdvd__0__left__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6, clsrel_Ring__and__Field_Olordered__ring_29, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, clsrel_Power_Orecpower_12, cls_Nat_Oadd__gr__0__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_1, clsarity_IntDef__Oint_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9, cls_Divides_Odvd__triv__left_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3, clsrel_Ring__and__Field_Oidom_19, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8, cls_Divides_Odvd__0__right_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22, clsrel_OrderedGroup_Olordered__ab__group__join_12, cls_IntDiv_Odvd__zminus__iff__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5, clsrel_Ring__and__Field_Ocomm__ring__1_11, clsrel_Ring__and__Field_Oordered__semidom_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsrel_Ring__and__Field_Oordered__idom_41, clsrel_Ring__and__Field_Osemiring__1__cancel_1, clsrel_Ring__and__Field_Oaxclass__abs__if_2, clsrel_Ring__and__Field_Oordered__ring__strict_9, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27, clsrel_Ring__and__Field_Oidom_3, clsrel_Ring__and__Field_Osemiring__1__cancel_2, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring_15, clsrel_Numeral_Onumber__ring_25, clsrel_Ring__and__Field_Osemiring__0__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15, clsrel_OrderedGroup_Olordered__ab__group__meet_7, cls_List_Olist_Odistinct__2__iff1_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Transitive__Closure_Or__into__rtrancl_0, clsrel_Numeral_Onumber__ring_0, clsrel_Ring__and__Field_Osemiring__1__cancel_11, clsrel_Ring__and__Field_Ocomm__semiring__0_9, clsarity_IntDef__Oint_10, clsrel_Ring__and__Field_Osemiring__0__cancel_2, clsrel_OrderedGroup_Olordered__ab__group_15, cls_Datatype__Universe_OdprodI_0, clsrel_OrderedGroup_Oab__group__add_2, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_List_Oappend__self__conv2__iff2_0, clsrel_Ring__and__Field_Oring_8, cls_List_Oappend__self__conv__iff2_0, cls_List_Oappend__same__eq__iff1_0, clsrel_Ring__and__Field_Oring_3, clsrel_Numeral_Onumber__ring_14, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Set_ODiffI_0, clsrel_OrderedGroup_Oab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__ring_20, clsrel_Ring__and__Field_Opordered__semiring_4, cls_Sum__Type_OInrI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3, clsarity_fun_1, clsrel_Ring__and__Field_Oring_11, cls_List_OlistsE_1, clsarity_nat_12, clsrel_Ring__and__Field_Oordered__ring__strict_17, clsrel_Ring__and__Field_Opordered__ring_4, clsrel_Ring__and__Field_Oordered__ring__strict_12, clsrel_OrderedGroup_Olordered__ab__group__join_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4, cls_Nat_OSuc__le__mono__iff2_0, clsrel_LOrder_Ojoin__semilorder_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_Set_OUn__empty__iff2_0, clsarity_IntDef__Oint_62, clsrel_Ring__and__Field_Oring__1_9, clsarity_IntDef__Oint_22, clsrel_OrderedGroup_Olordered__ab__group_10, clsrel_Ring__and__Field_Oordered__idom_30, cls_SetInterval_OgreaterThan__iff__iff1_0, clsarity_IntDef__Oint_5, clsrel_Ring__and__Field_Oring_12, cls_Set_OCompl__subset__Compl__iff__iff1_0, clsarity_nat_20, cls_Orderings_Oorder__less__irrefl__iff1_0, clsrel_Power_Orecpower_22, clsarity_IntDef__Oint_21, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1, clsrel_Ring__and__Field_Oordered__semiring__strict_14, clsarity_nat_5, cls_Datatype__Universe_Odsum__In1I_0, cls_Datatype__Universe_OuprodE_1, clsrel_Ring__and__Field_Oidom_30, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Ocomm__ring__1_18, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, clsrel_Ring__and__Field_Opordered__ring_8, clsrel_OrderedGroup_Opordered__ab__group__add_3, clsrel_Ring__and__Field_Osemiring__1_9, cls_List_Olistrel__Nil2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7, clsrel_OrderedGroup_Olordered__ab__group__join_4, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9, clsrel_LOrder_Olorder_1, cls_Relation_Orel__compI_0, clsarity_nat_42, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, clsrel_Ring__and__Field_Oordered__semidom_21, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Set_OUnionI_0, clsrel_Ring__and__Field_Oordered__idom_8, clsrel_Ring__and__Field_Osemiring__0_5, clsrel_OrderedGroup_Olordered__ab__group_11, clsrel_OrderedGroup_Olordered__ab__group__meet_3, clsrel_Ring__and__Field_Opordered__semiring_0, clsrel_OrderedGroup_Olordered__ab__group__abs_9, clsrel_Ring__and__Field_Opordered__comm__semiring_6, clsrel_Ring__and__Field_Ocomm__semiring__0_5, clsrel_OrderedGroup_Opordered__ab__semigroup__add_2, clsrel_Ring__and__Field_Ocomm__ring__1_22, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_14, clsrel_Ring__and__Field_Olordered__ring_6, clsrel_Ring__and__Field_Oordered__semiring__strict_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5, clsrel_Ring__and__Field_Oordered__semiring__strict_20, clsrel_Ring__and__Field_Ocomm__ring__1_9, clsrel_Ring__and__Field_Osemiring_3, clsrel_Numeral_Onumber__ring_3, clsarity_nat_31, cls_Datatype__Universe_OIn0__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_40, clsrel_OrderedGroup_Ocomm__monoid__add_3, clsrel_Ring__and__Field_Oordered__idom_25, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1, cls_Nat_OSuc__less__eq__iff1_0, cls_GCD_Ogcd__dvd2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23, clsrel_Power_Orecpower_8, cls_Relation_OdiagE_1, clsrel_Ring__and__Field_Oordered__ring__strict_0, clsarity_nat_9, clsrel_Ring__and__Field_Ocomm__ring__1_3, clsrel_Ring__and__Field_Opordered__semiring_11, clsrel_Ring__and__Field_Oordered__semidom_26, clsrel_Ring__and__Field_Ocomm__semiring__1_6, cls_IntDiv_Ozmod__eq__0D__dest_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18, clsrel_Ring__and__Field_Oordered__ring__strict_31, clsrel_Ring__and__Field_Oring__1_5, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, clsrel_Ring__and__Field_Oordered__idom_9, clsrel_Ring__and__Field_Osemiring__1_6, clsrel_Ring__and__Field_Ocomm__ring_5, clsrel_Ring__and__Field_Oidom_12, clsrel_Numeral_Onumber__ring_8, cls_Relation_OImage__singleton__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_10, clsrel_Ring__and__Field_Opordered__cancel__semiring_7, cls_List_ONil2__notin__lex__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Ocomm__semiring__1_9, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__ring__strict_34, clsrel_Ring__and__Field_Ocomm__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9, clsrel_Power_Orecpower_2, clsrel_Ring__and__Field_Olordered__ring_17, clsrel_Ring__and__Field_Oordered__semidom_15, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14, clsarity_nat_46, clsrel_Ring__and__Field_Oidom_16, cls_List_Oself__append__conv2__iff1_0, clsrel_Ring__and__Field_Olordered__ring_28, clsrel_Ring__and__Field_Oordered__semidom_5, clsrel_Ring__and__Field_Ocomm__semiring__0_1, clsrel_Ring__and__Field_Oordered__semidom_6, clsrel_Ring__and__Field_Oordered__semiring__strict_6, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_OrderedGroup_Opordered__ab__group__add_7, clsarity_IntDef__Oint_44, cls_Nat_Oneq0__conv__iff1_0, clsrel_Ring__and__Field_Oring_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, clsrel_Ring__and__Field_Opordered__ring_15, clsrel_Ring__and__Field_Olordered__ring_9, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, clsrel_OrderedGroup_Opordered__ab__group__add_5, clsrel_Ring__and__Field_Ocomm__semiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_22, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, clsrel_Ring__and__Field_Oordered__idom_33, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, clsrel_Ring__and__Field_Oordered__idom_44, clsrel_Ring__and__Field_Ocomm__semiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_37, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5, clsarity_nat_35, clsrel_Ring__and__Field_Oidom_8, clsrel_Ring__and__Field_Oidom_18, cls_List_Olist_Odistinct__1__iff1_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, clsrel_Ring__and__Field_Oordered__ring__strict_23, clsrel_Ring__and__Field_Oordered__semiring__strict_23, clsrel_Ring__and__Field_Oordered__ring__strict_29, clsrel_Ring__and__Field_Oordered__ring__strict_6, clsrel_Ring__and__Field_Oring__1_17, clsrel_OrderedGroup_Opordered__ab__group__add_13, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_Ring__and__Field_Opordered__comm__semiring_11, clsarity_IntDef__Oint_17, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3, cls_SetInterval_OatLeast__eq__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_12, clsrel_OrderedGroup_Olordered__ab__group_12, cls_Sum__Type_OPlusE_1, clsrel_Ring__and__Field_Oordered__semidom_29, clsrel_Ring__and__Field_Oordered__idom_0, cls_Set_OUnionE_0, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_Ring__and__Field_Osemiring__1_1, clsarity_IntDef__Oint_28, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, clsrel_Ring__and__Field_Osemiring__0_4, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_Divides_Odvd__1__left_0, cls_List_Oin__listsI_0, clsrel_Ring__and__Field_Ocomm__ring_7, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, clsrel_Ring__and__Field_Ocomm__ring_18, cls_IntDef_Onegative__zle_0, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, clsrel_Ring__and__Field_Oordered__idom_13, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Numeral_Onumber__ring_21, clsrel_Ring__and__Field_Oordered__idom_45, clsrel_OrderedGroup_Opordered__ab__group__add_0, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Power_Orecpower_20, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Oring__1_13, clsrel_Ring__and__Field_Osemiring__0__cancel_5, clsrel_OrderedGroup_Olordered__ab__group__join_10, clsarity_IntDef__Oint_41, clsrel_Ring__and__Field_Oordered__semiring__strict_0, clsarity_nat_24, cls_List_Oappend1__eq__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_0, clsrel_Ring__and__Field_Oidom_28, clsrel_Ring__and__Field_Oordered__idom_34, clsrel_Ring__and__Field_Osemiring_0, clsrel_Ring__and__Field_Opordered__ring_1, clsrel_Ring__and__Field_Oring_4, clsarity_IntDef__Oint_11, clsrel_Ring__and__Field_Oordered__semiring__strict_13, clsrel_Ring__and__Field_Opordered__semiring_9, clsrel_Ring__and__Field_Ocomm__semiring_3, clsrel_Ring__and__Field_Osemiring__1__cancel_8, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6, clsrel_Ring__and__Field_Olordered__ring_5, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsrel_Ring__and__Field_Oidom_27, clsrel_Ring__and__Field_Oordered__semidom_33, clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsrel_Ring__and__Field_Oidom_23, clsrel_Ring__and__Field_Olordered__ring_30, clsarity_nat_1, clsrel_Power_Orecpower_11, clsrel_Ring__and__Field_Oordered__idom_24, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, clsrel_LOrder_Omeet__semilorder_1, clsrel_Ring__and__Field_Oidom_4, clsarity_set_0, clsarity_IntDef__Oint_51, clsrel_Numeral_Onumber__ring_10, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0, cls_Nat_OSuc__not__Zero__iff1_0, clsrel_Numeral_Onumber__ring_26, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, clsarity_nat_4, clsrel_Ring__and__Field_Ocomm__ring__1_6, clsrel_Ring__and__Field_Opordered__ring_5, clsrel_Ring__and__Field_Oordered__idom_27, clsrel_Ring__and__Field_Oordered__ring__strict_13, clsrel_OrderedGroup_Opordered__ab__group__add_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, clsrel_Ring__and__Field_Opordered__ring_10, clsrel_Ring__and__Field_Olordered__ring_0, cls_Nat_Ole0_0, clsrel_OrderedGroup_Oab__semigroup__mult_1, cls_Nat_Oless__one__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_23, clsrel_Numeral_Onumber__ring_15, clsarity_IntDef__Oint_63, clsrel_Ring__and__Field_Oring__1_8, cls_Set_Osingleton__insert__inj__eq__iff1_0, clsarity_nat_19, cls_Sum__Type_OInl__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring_0, clsrel_Ring__and__Field_Oordered__semiring__strict_15, cls_Relation_OImage__singleton__iff__iff2_0, clsrel_Ring__and__Field_Olordered__ring_2, clsrel_Ring__and__Field_Ocomm__ring_14, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Osemiring__0__cancel_10, clsrel_Ring__and__Field_Oordered__semidom_30, clsrel_OrderedGroup_Ocomm__monoid__mult_4, clsrel_Ring__and__Field_Osemiring__1_5, clsrel_OrderedGroup_Olordered__ab__group__meet_8, clsrel_Ring__and__Field_Ocomm__semiring__0_8, cls_List_Olength__0__conv__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_5, clsrel_OrderedGroup_Omonoid__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2, clsrel_Ring__and__Field_Osemiring_4, clsarity_IntDef__Oint_12, clsrel_Ring__and__Field_Opordered__cancel__semiring_13, cls_Relation_OIdE_0, clsrel_Ring__and__Field_Oidom_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28, clsrel_Numeral_Onumber__ring_29, clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsarity_IntDef__Oint_55, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsrel_OrderedGroup_Opordered__ab__group__add_12, clsarity_IntDef__Oint_61, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_Numeral_Onumber__ring_9, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Olordered__ring_20, clsarity_IntDef__Oint_50, clsrel_Ring__and__Field_Opordered__ring_21, clsrel_Ring__and__Field_Ocomm__semiring__1_5, clsrel_OrderedGroup_Oab__group__add_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Oordered__idom_16, clsrel_Ring__and__Field_Osemiring__0_3, clsrel_OrderedGroup_Olordered__ab__group__join_5, clsrel_Ring__and__Field_Oring__1_16, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Numeral_Onumber__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Olordered__ring_16, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, clsrel_Ring__and__Field_Oring__1_3, cls_Set_OIntE_0, clsarity_nat_30, cls_Relation_Orel__compE_1, clsarity_set_4, clsrel_Ring__and__Field_Oring__1_10, cls_List_Oappend__is__Nil__conv__iff1_1, clsrel_Ring__and__Field_Oring__1_4, clsrel_Numeral_Onumber__ring_18, clsrel_Ring__and__Field_Ocomm__ring__1_17, clsrel_Ring__and__Field_Osemiring__0__cancel_0, clsrel_Ring__and__Field_Oordered__semidom_14, clsrel_Ring__and__Field_Oordered__ring__strict_2, clsarity_nat_41, clsrel_Ring__and__Field_Oordered__ring__strict_30, cls_Finite__Set_Ofinite__Un__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__abs_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__ring__1_28, clsrel_Ring__and__Field_Olordered__ring_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozminus__dvd__iff__iff2_0, clsarity_IntDef__Oint_9, clsrel_Ring__and__Field_Oordered__semiring__strict_18, clsrel_Ring__and__Field_Opordered__comm__semiring_4, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0, clsrel_Ring__and__Field_Olordered__ring_27, cls_Set_OinsertCI_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, clsrel_Ring__and__Field_Olordered__ring_13, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__ring_16, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0, clsrel_Power_Orecpower_19, clsrel_OrderedGroup_Olordered__ab__group__join_1, cls_List_Oappend__self__conv__iff1_0
% 16.73/4.84  % No. of inferences in proof: 2341
% 16.73/4.84  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4286 ms resp. 3161 ms w/o parsing
% 18.94/5.23  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.94/5.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------