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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SET825-1 : 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 : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:31:00 AM UTC 2026

% Result   : Unsatisfiable 21.86s 6.06s
% Output   : Refutation 24.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  791
% Syntax   : Number of formulae    : 1583 ( 357 unt;   0 typ;   0 def)
%            Number of atoms       : 2937 ( 292 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 11670 (1354   ~;1354   |;   0   &;8962   @)
%                                         (   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     :  170 ( 168 usr;  15 con; 0-6 aty)
%            Number of variables   : 2588 (   0   ^;2588   !;   0   ?;2588   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_Q_decl,type,
    v_Q: $i > $o ).

thf(v_n_decl,type,
    v_n: $i ).

thf(v_m_decl,type,
    v_m: $i ).

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

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

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

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

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

thf(v_xa_decl,type,
    v_xa: $i > $i ).

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

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

thf(c_Datatype__Universe_Ousum_decl,type,
    c_Datatype__Universe_Ousum: $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_Main_OusumE__2_decl,type,
    c_Main_OusumE__2: $i > $i > $i > $i > $i ).

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

thf(c_Main_OusumE__1_decl,type,
    c_Main_OusumE__1: $i > $i > $i > $i > $i ).

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

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_OatLeast_decl,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

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

thf(class_Finite__Set_Ofinite_decl,type,
    class_Finite__Set_Ofinite: $i > $o ).

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

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

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

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

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

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

thf(tc_IntDef_Oint_decl,type,
    tc_IntDef_Oint: $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_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_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_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $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_Ring__and__Field_Ocomm__semiring__1__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

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

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

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

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

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

thf(class_OrderedGroup_Osemigroup__mult_decl,type,
    class_OrderedGroup_Osemigroup__mult: $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_Ring__and__Field_Ocomm__semiring_decl,type,
    class_Ring__and__Field_Ocomm__semiring: $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_Ocomm__semiring__0__cancel_decl,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

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

thf(c_List_Oremdups_decl,type,
    c_List_Oremdups: $i > $i > $i ).

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

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

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

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

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

thf(class_Ring__and__Field_Osemiring__1_decl,type,
    class_Ring__and__Field_Osemiring__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__cancel__semiring_decl,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

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

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

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

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

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

thf(tc_bool_decl,type,
    tc_bool: $i ).

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

thf(tc_Datatype_Ooption_decl,type,
    tc_Datatype_Ooption: $i > $i ).

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

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

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

thf(c_1_decl,type,
    c_1: $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_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(tc_sum_decl,type,
    tc_sum: $i > $i > $i ).

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

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

thf(tc_Product__Type_Ounit_decl,type,
    tc_Product__Type_Ounit: $i ).

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

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

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

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

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

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_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_Datatype__Universe_Odsum_decl,type,
    c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).

thf(c_Main_OdsumE__1_decl,type,
    c_Main_OdsumE__1: $i > $i > $i > $i > $i ).

thf(c_Main_OdsumE__2_decl,type,
    c_Main_OdsumE__2: $i > $i > $i > $i > $i ).

thf(c_Main_OdsumE__3_decl,type,
    c_Main_OdsumE__3: $i > $i > $i > $i > $i ).

thf(c_Main_OdsumE__4_decl,type,
    c_Main_OdsumE__4: $i > $i > $i > $i > $i ).

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

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

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

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

thf(c_Main_Olistrel__Cons1__1_decl,type,
    c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).

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

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

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

thf(c_Transitive__Closure_Ortrancl_decl,type,
    c_Transitive__Closure_Ortrancl: $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_Datatype_Oo2s_decl,type,
    c_Datatype_Oo2s: $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_Infinite__Set_Oatmost__one_decl,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(c_Main_Olistrel__Cons2__1_decl,type,
    c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).

thf(c_Main_Olistrel__Cons2__2_decl,type,
    c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).

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_Relation_OId_decl,type,
    c_Relation_OId: $i ).

thf(c_Datatype__Universe_Odprod_decl,type,
    c_Datatype__Universe_Odprod: $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__3_decl,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

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

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

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

thf(c_Main_OdiagE__1_decl,type,
    c_Main_OdiagE__1: $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__4_decl,type,
    c_Main_OdprodE__4: $i > $i > $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_OImageE__1_decl,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

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_Main_OIdE__1_decl,type,
    c_Main_OIdE__1: $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_Main_Olistrel__Cons1__2_decl,type,
    c_Main_Olistrel__Cons1__2: $i > $i > $i > $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(716,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(2199,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(657,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(2094,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(111,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(1024,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(285,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(1369,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)],[285]) ).

thf(765,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(2295,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)],[765]) ).

thf(151,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(1105,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(468,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(1729,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(22,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(846,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(528,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(1850,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(594,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(1982,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)],[594]) ).

thf(67,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(941,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_less ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(514,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(1818,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)],[514]) ).

thf(380,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(1554,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)],[380]) ).

thf(739,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(2250,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)],[739]) ).

thf(697,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(2163,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)],[697]) ).

thf(43,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(892,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)],[43]) ).

thf(544,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(1879,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)],[544]) ).

thf(269,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(1337,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)],[269]) ).

thf(664,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(2109,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)],[664]) ).

thf(677,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(2131,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(329,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(1454,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(648,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(2072,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)],[648]) ).

thf(489,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(1767,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)],[489]) ).

thf(191,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(1179,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)],[191]) ).

thf(785,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(2331,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)],[785]) ).

thf(579,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(1956,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(576,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(1950,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(1549,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(207,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(1211,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(545,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(1882,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)],[545]) ).

thf(728,axiom,
    tc_nat @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(2231,plain,
    tc_nat @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(364,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(1522,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)],[364]) ).

thf(643,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(2062,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(323,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(1443,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)],[323]) ).

thf(413,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(1618,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(300,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(1401,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(613,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(2014,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)],[613]) ).

thf(204,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(1205,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(399,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(1591,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(172,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(1142,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)],[172]) ).

thf(252,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(1305,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)],[252]) ).

thf(319,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(1437,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)],[319]) ).

thf(119,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(1041,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(480,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(1750,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)],[480]) ).

thf(86,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(977,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)],[86]) ).

thf(180,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(1158,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)],[180]) ).

thf(774,axiom,
    tc_nat @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(2309,plain,
    tc_nat @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(311,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(1422,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)],[311]) ).

thf(570,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(1939,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(738,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(2248,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)],[738]) ).

thf(503,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(1793,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(369,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(1533,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)],[369]) ).

thf(188,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(1173,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(345,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(1486,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)],[345]) ).

thf(407,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(1608,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)],[407]) ).

thf(431,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(1655,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)],[431]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(1756,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(626,axiom,
    tc_nat @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(2035,plain,
    tc_nat @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(471,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(1735,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(684,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(2141,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)],[684]) ).

thf(561,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(1919,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)],[561]) ).

thf(69,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(945,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)],[69]) ).

thf(630,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(2042,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)],[630]) ).

thf(62,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(930,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)],[62]) ).

thf(331,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(1458,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(350,axiom,
    tc_IntDef_Oint @ class_HOL_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(1497,plain,
    tc_IntDef_Oint @ class_HOL_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(456,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(1705,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(137,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(1078,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)],[137]) ).

thf(313,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(1426,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)],[313]) ).

thf(183,axiom,
    tc_IntDef_Oint @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(1164,plain,
    tc_IntDef_Oint @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(605,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(1999,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(700,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(2168,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)],[700]) ).

thf(230,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(1260,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(129,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(1063,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(578,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(1954,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)],[578]) ).

thf(278,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(1354,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)],[278]) ).

thf(686,axiom,
    tc_nat @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(2146,plain,
    tc_nat @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(146,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(1095,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(478,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(1746,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(322,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(1441,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)],[322]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(1613,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(280,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(1359,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(293,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(1386,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)],[293]) ).

thf(652,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(2082,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)],[652]) ).

thf(339,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(1475,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(508,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(1803,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(164,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(1127,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)],[164]) ).

thf(498,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(1782,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)],[498]) ).

thf(295,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(1391,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)],[295]) ).

thf(391,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(1576,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)],[391]) ).

thf(617,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(2020,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

thf(841,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(84,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(973,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(122,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(1046,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(430,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(1650,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)],[430]) ).

thf(427,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(1645,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)],[427]) ).

thf(562,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(1921,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)],[562]) ).

thf(646,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(2067,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)],[646]) ).

thf(585,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(1967,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(681,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(2136,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(553,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(1904,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)],[553]) ).

thf(362,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(1518,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)],[362]) ).

thf(455,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(1703,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)],[455]) ).

thf(214,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(1228,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(343,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(1482,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(227,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(1254,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)],[227]) ).

thf(418,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(1628,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)],[418]) ).

thf(243,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(1287,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(458,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(1709,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)],[458]) ).

thf(315,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(1430,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(540,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(1871,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(261,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(1323,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)],[261]) ).

thf(6,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(802,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)],[6]) ).

thf(518,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(1826,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)],[518]) ).

thf(256,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(1313,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)],[256]) ).

thf(711,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(2185,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)],[711]) ).

thf(601,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(1992,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)],[601]) ).

thf(71,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(949,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(125,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(1055,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)],[125]) ).

thf(304,axiom,
    tc_IntDef_Oint @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(1409,plain,
    tc_IntDef_Oint @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(485,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(1760,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)],[485]) ).

thf(249,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(1298,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)],[249]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(1330,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(534,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(1860,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)],[534]) ).

thf(232,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(1264,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)],[232]) ).

thf(358,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(1511,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(753,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

thf(2274,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(917,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(521,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(1832,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)],[521]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(934,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(197,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(1191,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)],[197]) ).

thf(127,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(1059,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(167,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(1132,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)],[167]) ).

thf(375,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(1545,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)],[375]) ).

thf(12,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(817,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)],[12]) ).

thf(24,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(853,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)],[24]) ).

thf(290,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(1379,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)],[290]) ).

thf(360,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(1514,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(175,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(1147,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)],[175]) ).

thf(634,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(2049,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)],[634]) ).

thf(259,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(1319,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(341,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(1479,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)],[341]) ).

thf(104,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(1013,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(387,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(1568,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)],[387]) ).

thf(694,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(2158,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)],[694]) ).

thf(216,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(1232,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(274,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(1347,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)],[274]) ).

thf(389,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(1572,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(475,axiom,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(1741,plain,
    tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(37,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(881,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)],[37]) ).

thf(619,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

thf(2024,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(425,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(1641,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(769,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(2301,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)],[769]) ).

thf(349,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(1494,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)],[349]) ).

thf(609,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(2007,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(731,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(2237,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)],[731]) ).

thf(59,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(924,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(287,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(1373,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)],[287]) ).

thf(743,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(2259,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)],[743]) ).

thf(309,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(1418,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(519,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(1828,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(177,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(1151,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(625,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(2034,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)],[625]) ).

thf(581,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(1960,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(50,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(905,plain,
    ! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(574,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(1946,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)],[574]) ).

thf(334,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(1465,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)],[334]) ).

thf(782,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(2324,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)],[782]) ).

thf(621,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(2027,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)],[621]) ).

thf(512,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(1811,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)],[512]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).

thf(1450,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(153,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(1109,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(420,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(1632,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(169,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(1136,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)],[169]) ).

thf(17,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(834,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)],[17]) ).

thf(536,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(1864,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)],[536]) ).

thf(671,axiom,
    tc_nat @ class_Power_Orecpower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(2122,plain,
    tc_nat @ class_Power_Orecpower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(292,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(1383,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)],[292]) ).

thf(108,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(1020,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(741,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) ) )
      | ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ 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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).

thf(2254,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) ) )
      | ( A
        = ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ 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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(394,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(1581,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)],[394]) ).

thf(787,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

thf(2335,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).

thf(966,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(193,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(1183,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)],[193]) ).

thf(241,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(1283,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)],[241]) ).

thf(641,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(2058,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)],[641]) ).

thf(186,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(1169,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)],[186]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).

thf(1377,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(756,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(2281,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)],[756]) ).

thf(35,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(877,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(547,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(1886,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(134,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(1072,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)],[134]) ).

thf(202,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(1201,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(691,axiom,
    tc_nat @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(2154,plain,
    tc_nat @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(718,axiom,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(2205,plain,
    ! [A: $i] :
      ( c_0
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(385,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(1564,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(366,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(1526,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)],[366]) ).

thf(682,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(2137,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)],[682]) ).

thf(607,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(2002,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)],[607]) ).

thf(96,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(998,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)],[96]) ).

thf(273,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(1345,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(91,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(988,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(759,axiom,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(2286,plain,
    ! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(661,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(2103,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(1405,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(1697,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(221,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(1242,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)],[221]) ).

thf(611,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

thf(2011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(449,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(1691,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(2,negated_conjecture,
    ~ ( v_m @ v_Q ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(793,plain,
    ~ ( v_m @ v_Q ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(178,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(1153,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)],[178]) ).

thf(668,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(2118,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)],[668]) ).

thf(9,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(810,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(633,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(2047,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)],[633]) ).

thf(131,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(1067,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)],[131]) ).

thf(538,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(1868,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(126,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(1057,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(135,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(1074,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(405,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(1604,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)],[405]) ).

thf(337,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(1470,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(559,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(1915,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(255,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(1311,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(729,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(2232,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)],[729]) ).

thf(773,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(2307,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)],[773]) ).

thf(642,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(2061,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(606,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(2000,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(422,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(1636,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)],[422]) ).

thf(237,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(1274,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)],[237]) ).

thf(745,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(2264,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)],[745]) ).

thf(272,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(1343,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(109,axiom,
    tc_bool @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).

thf(1021,plain,
    tc_bool @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(393,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(1580,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(687,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(2147,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)],[687]) ).

thf(436,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(1666,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(678,axiom,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

thf(2132,plain,
    tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(219,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(1238,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)],[219]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).

thf(1560,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(1900,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(465,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(1723,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(53,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(910,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)],[53]) ).

thf(75,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(957,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)],[75]) ).

thf(211,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(1223,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)],[211]) ).

thf(44,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(894,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)],[44]) ).

thf(161,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1123,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(28,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(862,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)],[28]) ).

thf(388,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(1570,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(442,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(1676,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)],[442]) ).

thf(679,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(2133,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)],[679]) ).

thf(353,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(1502,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(13,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(820,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)],[13]) ).

thf(517,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(1824,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)],[517]) ).

thf(414,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(1619,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(624,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(2032,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)],[624]) ).

thf(11,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(815,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)],[11]) ).

thf(283,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(1365,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)],[283]) ).

thf(447,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(1687,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(416,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(1624,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(706,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(2179,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(776,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(2313,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)],[776]) ).

thf(240,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(1281,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(421,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(1634,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)],[421]) ).

thf(245,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(1291,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)],[245]) ).

thf(556,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(1910,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)],[556]) ).

thf(152,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(1106,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)],[152]) ).

thf(115,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

thf(1032,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(404,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(1602,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)],[404]) ).

thf(586,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(1968,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(36,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(879,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)],[36]) ).

thf(548,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(1888,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)],[548]) ).

thf(248,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(1296,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(500,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(1787,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)],[500]) ).

thf(708,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(2181,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(199,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(1195,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(720,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(2211,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(303,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(1407,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(768,axiom,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(2300,plain,
    tc_nat @ class_LOrder_Ojoin__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(217,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(1234,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(486,axiom,
    tc_IntDef_Oint @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(1762,plain,
    tc_IntDef_Oint @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(1328,plain,
    ! [A: $i] :
      ( ( A @ class_Nat_Opower )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(288,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(1375,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)],[288]) ).

thf(531,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

thf(1856,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(440,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(1672,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)],[440]) ).

thf(543,axiom,
    tc_IntDef_Oint @ class_Divides_Odiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(1878,plain,
    tc_IntDef_Oint @ class_Divides_Odiv,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(31,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(869,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)],[31]) ).

thf(158,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(1118,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)],[158]) ).

thf(749,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(2268,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)],[749]) ).

thf(298,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(1397,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)],[298]) ).

thf(736,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(2245,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(276,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(1350,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)],[276]) ).

thf(33,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(874,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)],[33]) ).

thf(667,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(2115,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(235,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(1270,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)],[235]) ).

thf(492,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(1772,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)],[492]) ).

thf(154,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(1111,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)],[154]) ).

thf(587,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(1970,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(87,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(980,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)],[87]) ).

thf(351,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(1498,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)],[351]) ).

thf(397,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(1587,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).

thf(1540,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(100,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(1006,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)],[100]) ).

thf(170,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(1138,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)],[170]) ).

thf(463,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(1719,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(445,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(1683,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)],[445]) ).

thf(39,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(884,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(181,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(1160,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)],[181]) ).

thf(281,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(1361,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)],[281]) ).

thf(246,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(1292,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

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(901,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(312,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(1424,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)],[312]) ).

thf(502,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(1791,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(113,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(1028,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)],[113]) ).

thf(139,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(1082,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(618,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(2023,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(583,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(1964,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(572,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(1942,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(433,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(1659,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(474,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(1739,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)],[474]) ).

thf(332,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(1461,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)],[332]) ).

thf(307,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(1414,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)],[307]) ).

thf(637,axiom,
    tc_nat @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(2053,plain,
    tc_nat @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(524,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(1842,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(628,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(2038,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)],[628]) ).

thf(325,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(1446,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(106,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(1016,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(1207,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Ojoin__semilorder )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(653,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(2085,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)],[653]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1039,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(82,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(970,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)],[82]) ).

thf(778,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(2317,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)],[778]) ).

thf(477,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(1744,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)],[477]) ).

thf(18,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(837,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)],[18]) ).

thf(95,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(997,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)],[95]) ).

thf(148,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(1099,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(771,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(2304,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(330,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(1456,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)],[330]) ).

thf(233,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(1266,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(734,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(2243,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(568,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(1932,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)],[568]) ).

thf(89,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(984,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)],[89]) ).

thf(506,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(1799,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)],[506]) ).

thf(595,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(1984,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)],[595]) ).

thf(461,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(1715,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(592,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(1979,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(751,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2272,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(683,axiom,
    tc_nat @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(2140,plain,
    tc_nat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(296,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(1393,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(365,axiom,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(1525,plain,
    tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(758,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(2285,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)],[758]) ).

thf(156,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(1114,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(438,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(1668,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)],[438]) ).

thf(589,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(1974,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(128,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(1060,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)],[128]) ).

thf(124,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(1050,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)],[124]) ).

thf(98,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(1002,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(529,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

thf(1852,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(636,axiom,
    tc_nat @ class_Nat_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(2052,plain,
    tc_nat @ class_Nat_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(403,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(1599,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)],[403]) ).

thf(223,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(1246,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)],[223]) ).

thf(267,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(1333,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1,negated_conjecture,
    v_n @ v_Q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(792,plain,
    v_n @ v_Q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(496,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(1779,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(451,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(1695,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)],[451]) ).

thf(57,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(921,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)],[57]) ).

thf(650,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(2076,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)],[650]) ).

thf(116,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(1035,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(133,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(1071,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(195,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(1187,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)],[195]) ).

thf(435,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(1663,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)],[435]) ).

thf(713,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(2189,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(41,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(888,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(60,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(926,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(317,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(1434,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(532,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(1857,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)],[532]) ).

thf(600,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(1991,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)],[600]) ).

thf(258,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(1318,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)],[258]) ).

thf(141,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(1086,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)],[141]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).

thf(938,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(719,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(2208,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)],[719]) ).

thf(7,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(805,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)],[7]) ).

thf(640,axiom,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(2057,plain,
    tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(526,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(1846,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)],[526]) ).

thf(112,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(1026,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(550,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(1895,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)],[550]) ).

thf(185,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(1167,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)],[185]) ).

thf(73,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(953,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)],[73]) ).

thf(194,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(1185,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)],[194]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ ( A @ v_x @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(794,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ ( A @ v_x @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(788,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(2338,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)],[788]) ).

thf(603,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(1996,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)],[603]) ).

thf(429,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(1648,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(467,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(1727,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(150,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(1103,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)],[150]) ).

thf(688,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(2149,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)],[688]) ).

thf(565,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(1927,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(670,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(2121,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(730,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

thf(2235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(51,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(906,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(239,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(1278,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)],[239]) ).

thf(554,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(1906,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(482,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(1754,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(763,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(2292,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(250,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(1301,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)],[250]) ).

thf(401,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(1595,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)],[401]) ).

thf(85,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(975,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(411,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(1615,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)],[411]) ).

thf(21,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(843,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)],[21]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(1752,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(566,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(1929,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(614,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(2016,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)],[614]) ).

thf(294,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(1388,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)],[294]) ).

thf(34,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(875,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(370,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(1535,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)],[370]) ).

thf(301,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(1403,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(584,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(1965,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)],[584]) ).

thf(363,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(1520,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(162,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(1124,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(725,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(2225,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(546,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(1884,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(504,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(1795,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(454,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(1701,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)],[454]) ).

thf(228,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(1256,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)],[228]) ).

thf(213,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(1226,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)],[213]) ).

thf(346,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(1488,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(65,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(936,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)],[65]) ).

thf(724,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(2220,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)],[724]) ).

thf(286,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(1371,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(470,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(1733,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(604,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(1997,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)],[604]) ).

thf(266,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(1332,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(144,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(1092,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(56,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(919,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(229,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(1258,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)],[229]) ).

thf(70,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(947,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)],[70]) ).

thf(423,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(1638,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)],[423]) ).

thf(314,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(1428,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)],[314]) ).

thf(696,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(2161,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)],[696]) ).

thf(622,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(2029,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(783,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(2326,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)],[783]) ).

thf(457,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(1707,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(764,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(2293,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)],[764]) ).

thf(699,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(2166,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)],[699]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).

thf(1090,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(779,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(2319,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(279,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(1356,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)],[279]) ).

thf(651,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

thf(2079,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(206,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(1209,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(16,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(831,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)],[16]) ).

thf(722,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(2214,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)],[722]) ).

thf(123,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(1048,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)],[123]) ).

thf(275,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(1349,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(173,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(1144,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(491,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(1771,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)],[491]) ).

thf(160,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(1122,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(320,axiom,
    tc_IntDef_Oint @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(1439,plain,
    tc_IntDef_Oint @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(189,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(1175,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(689,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(2151,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)],[689]) ).

thf(727,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(2229,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)],[727]) ).

thf(390,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(1574,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)],[390]) ).

thf(103,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(1011,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)],[103]) ).

thf(742,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(2257,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)],[742]) ).

thf(398,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(1589,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(348,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(1492,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)],[348]) ).

thf(767,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(2299,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(120,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(1043,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(507,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(1801,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)],[507]) ).

thf(715,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(2197,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)],[715]) ).

thf(253,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(1307,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(709,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(2182,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)],[709]) ).

thf(138,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(1080,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(270,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(1339,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)],[270]) ).

thf(26,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(858,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(665,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(2111,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)],[665]) ).

thf(419,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(1630,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(748,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(2267,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(469,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(1731,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(535,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(1862,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(23,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(848,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)],[23]) ).

thf(262,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(1325,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(54,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(915,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(381,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(1556,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(755,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(2278,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)],[755]) ).

thf(515,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(1820,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)],[515]) ).

thf(42,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(890,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(437,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(1667,plain,
    ! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(707,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(2180,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)],[707]) ).

thf(676,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(2129,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)],[676]) ).

thf(791,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(2343,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)],[791]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

thf(799,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(182,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(1162,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)],[182]) ).

thf(176,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(1149,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(79,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(964,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(68,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(943,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(110,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(1022,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)],[110]) ).

thf(740,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(2252,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)],[740]) ).

thf(190,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(1177,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)],[190]) ).

thf(291,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(1381,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)],[291]) ).

thf(784,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(2329,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)],[784]) ).

thf(63,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(932,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(577,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(1952,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)],[577]) ).

thf(187,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(1171,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)],[187]) ).

thf(649,axiom,
    tc_nat @ class_Wellfounded__Recursion_Owellorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).

thf(2075,plain,
    tc_nat @ class_Wellfounded__Recursion_Owellorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(201,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(1198,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)],[201]) ).

thf(453,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(1699,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)],[453]) ).

thf(208,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(1213,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)],[208]) ).

thf(426,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(1643,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)],[426]) ).

thf(38,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(883,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(644,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(2064,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)],[644]) ).

thf(155,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(1113,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(340,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(1477,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(660,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(2101,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)],[660]) ).

thf(225,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(1250,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(770,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(2303,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(693,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(2156,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)],[693]) ).

thf(58,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(922,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)],[58]) ).

thf(509,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(1805,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)],[509]) ).

thf(384,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(1562,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(721,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(2212,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)],[721]) ).

thf(76,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(959,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)],[76]) ).

thf(702,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(2171,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)],[702]) ).

thf(635,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(2051,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(121,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(1044,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(324,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(1445,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(367,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(1528,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)],[367]) ).

thf(90,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(986,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(761,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(2288,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)],[761]) ).

thf(494,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(1775,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(735,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(2244,plain,
    ! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(97,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(1000,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)],[97]) ).

thf(136,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(1076,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)],[136]) ).

thf(417,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(1626,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(732,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(2239,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)],[732]) ).

thf(395,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(1583,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)],[395]) ).

thf(511,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(1809,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(658,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(2096,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)],[658]) ).

thf(541,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(1873,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)],[541]) ).

thf(203,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(1203,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)],[203]) ).

thf(335,axiom,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(1467,plain,
    ! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(4,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ c_Suc @ ( A @ v_x @ c_Suc @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(795,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ c_Suc @ ( A @ v_x @ c_Suc @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(310,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(1420,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)],[310]) ).

thf(673,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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) ) )
      | ( 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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ 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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).

thf(2124,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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) ) )
      | ( 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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ 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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(168,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
      | ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(338,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(1472,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)],[338]) ).

thf(580,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(1958,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(378,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(1551,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)],[378]) ).

thf(638,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(2054,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)],[638]) ).

thf(575,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(1948,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)],[575]) ).

thf(484,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(1758,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(663,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(2107,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)],[663]) ).

thf(10,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(812,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)],[10]) ).

thf(357,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(1509,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)],[357]) ).

thf(599,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(1990,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)],[599]) ).

thf(717,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(2202,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(786,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(2333,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)],[786]) ).

thf(174,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(1145,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(107,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(1018,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)],[107]) ).

thf(81,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(968,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(192,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(1181,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)],[192]) ).

thf(14,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(823,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)],[14]) ).

thf(25,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(855,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)],[25]) ).

thf(361,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(1516,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)],[361]) ).

thf(32,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(872,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)],[32]) ).

thf(212,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(1225,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(428,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(1647,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(704,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(2175,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)],[704]) ).

thf(497,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(1780,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)],[497]) ).

thf(368,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(1531,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)],[368]) ).

thf(93,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(993,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(376,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(1547,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(479,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(1748,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)],[479]) ).

thf(409,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(1611,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)],[409]) ).

thf(179,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(1156,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(386,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(1566,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)],[386]) ).

thf(685,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(2143,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(571,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(1941,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(226,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(1252,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)],[226]) ).

thf(215,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(1230,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)],[215]) ).

thf(344,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(1484,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)],[344]) ).

thf(695,axiom,
    tc_nat @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(2160,plain,
    tc_nat @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(459,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(1711,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)],[459]) ).

thf(656,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(2092,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)],[656]) ).

thf(328,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(1452,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(539,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(1869,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(499,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(1785,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)],[499]) ).

thf(231,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(1262,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(631,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(2044,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(166,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(1130,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)],[166]) ).

thf(501,axiom,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(1790,plain,
    tc_IntDef_Oint @ class_Numeral_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(597,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( 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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).

thf(1987,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( 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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(1432,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(698,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(2165,plain,
    tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(754,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(2276,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)],[754]) ).

thf(723,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(2219,plain,
    tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(675,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(2128,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(520,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(1830,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)],[520]) ).

thf(487,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(1763,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)],[487]) ).

thf(372,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(1538,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)],[372]) ).

thf(72,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(951,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(8,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(808,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)],[8]) ).

thf(242,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(1285,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)],[242]) ).

thf(473,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(1738,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(210,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(1218,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)],[210]) ).

thf(569,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(1934,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)],[569]) ).

thf(666,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(2113,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(593,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(1981,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(354,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(1504,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_LOrder_Omeet__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(101,axiom,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1008,plain,
    ! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).

thf(1272,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(747,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(2266,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(639,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(2056,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(737,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(2247,plain,
    tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(374,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(1543,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)],[374]) ).

thf(488,axiom,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(1766,plain,
    tc_IntDef_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(588,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(1972,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)],[588]) ).

thf(780,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(2320,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(355,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(1506,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)],[355]) ).

thf(396,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(1585,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(145,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

thf(1094,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(171,axiom,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(1140,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(439,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(1670,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(505,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(1797,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)],[505]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(1717,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(623,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(2030,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)],[623]) ).

thf(220,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(1240,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(92,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(991,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(412,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(1617,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(612,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(2013,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(523,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(1839,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)],[523]) ).

thf(654,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(2088,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(632,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(2045,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)],[632]) ).

thf(446,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(1685,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(379,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(1553,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)],[379]) ).

thf(714,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(2194,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)],[714]) ).

thf(306,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(1412,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)],[306]) ).

thf(209,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(1216,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)],[209]) ).

thf(163,axiom,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(1126,plain,
    tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(537,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(1866,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(1807,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(257,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(1316,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oone )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(140,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(1084,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)],[140]) ).

thf(260,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(1321,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)],[260]) ).

thf(522,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(1834,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)],[522]) ).

thf(558,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(1913,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(775,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(2310,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)],[775]) ).

thf(525,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(1844,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(49,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(903,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)],[49]) ).

thf(326,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(1448,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(712,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(2187,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)],[712]) ).

thf(196,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(1189,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(772,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(2305,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)],[772]) ).

thf(790,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(2342,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(244,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(1289,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(726,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) ) )
      | ( 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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).

thf(2226,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 @ ( A @ ( C @ c_Main_OdsumE__4 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OdsumE__3 ) ) ) @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) ) )
      | ( 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 @ ( A @ ( B @ c_Main_OdsumE__2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ c_Main_OdsumE__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_Odsum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(238,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(1276,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(263,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(1326,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)],[263]) ).

thf(762,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(2290,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)],[762]) ).

thf(680,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(2135,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(356,axiom,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(1508,plain,
    tc_IntDef_Oint @ class_LOrder_Olorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(342,axiom,
    tc_IntDef_Oint @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(1481,plain,
    tc_IntDef_Oint @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(149,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(1101,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)],[149]) ).

thf(608,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(2004,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)],[608]) ).

thf(620,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).

thf(2026,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(530,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(1854,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(77,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(961,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(464,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(1721,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)],[464]) ).

thf(78,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(963,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(752,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(2273,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)],[752]) ).

thf(703,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(2174,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(757,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(2283,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)],[757]) ).

thf(271,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(1341,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)],[271]) ).

thf(45,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(896,plain,
    tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(659,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(2098,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)],[659]) ).

thf(441,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(1674,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(424,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(1639,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)],[424]) ).

thf(222,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(1244,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(516,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(1822,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)],[516]) ).

thf(94,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(995,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)],[94]) ).

thf(382,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(1558,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)],[382]) ).

thf(690,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(2152,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)],[690]) ).

thf(744,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

thf(2262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
      | ~ ( D @ ( C @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(610,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(2009,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)],[610]) ).

thf(114,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(1030,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)],[114]) ).

thf(448,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(1689,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)],[448]) ).

thf(495,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(1777,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(247,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(1294,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(321,axiom,
    tc_IntDef_Oint @ class_HOL_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(1440,plain,
    tc_IntDef_Oint @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(645,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(2066,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)],[645]) ).

thf(198,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(1193,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(710,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(2183,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)],[710]) ).

thf(359,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(1513,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(669,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(2120,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(777,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(2315,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)],[777]) ).

thf(602,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).

thf(1994,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(616,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(2019,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)],[616]) ).

thf(47,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(899,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(434,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(1661,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(549,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(1893,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)],[549]) ).

thf(627,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(2036,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)],[627]) ).

thf(254,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(1309,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(672,axiom,
    tc_nat @ class_HOL_Otimes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(2123,plain,
    tc_nat @ class_HOL_Otimes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(760,axiom,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(2287,plain,
    tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(493,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(1774,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(466,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(1725,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Ozero )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(392,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(1578,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(443,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(1678,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)],[443]) ).

thf(692,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(2155,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(147,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

thf(1097,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(297,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(1395,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(1593,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oorder )
      | ~ ( A @ class_LOrder_Olorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(542,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(1876,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(224,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(1248,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)],[224]) ).

thf(30,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(867,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)],[30]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).

thf(865,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(157,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(1116,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(555,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(1908,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(251,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(1303,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)],[251]) ).

thf(596,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(1986,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(598,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(1989,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(282,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(1363,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)],[282]) ).

thf(513,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(1816,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(432,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(1657,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(200,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(1197,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(655,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(2091,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

thf(828,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
      | ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(130,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(1065,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)],[130]) ).

thf(629,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(2040,plain,
    ~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(74,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(955,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)],[74]) ).

thf(408,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(1610,plain,
    ! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(318,axiom,
    tc_IntDef_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(1436,plain,
    tc_IntDef_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(533,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(1859,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(268,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(1335,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)],[268]) ).

thf(450,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(1693,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(647,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(2070,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)],[647]) ).

thf(46,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(897,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)],[46]) ).

thf(305,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(1410,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)],[305]) ).

thf(789,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(2340,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(184,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(1165,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(40,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(886,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(1742,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(61,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(928,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__mult )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(277,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(1352,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(234,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(1268,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)],[234]) ).

thf(27,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(860,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)],[27]) ).

thf(371,axiom,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(1537,plain,
    tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(746,axiom,
    tc_nat @ class_HOL_Oplus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(2265,plain,
    tc_nat @ class_HOL_Oplus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(590,axiom,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(1976,plain,
    tc_IntDef_Oint @ class_Parity_Oeven__odd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(52,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(908,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(564,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(1925,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(460,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(1713,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)],[460]) ).

thf(552,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(1902,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)],[552]) ).

thf(159,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(1120,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(567,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(1930,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)],[567]) ).

thf(19,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(839,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(218,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(1236,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Oplus )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(733,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(2241,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)],[733]) ).

thf(674,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(2127,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(591,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(1977,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Osemigroup__add )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(165,axiom,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(1129,plain,
    tc_IntDef_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(352,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(1500,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Omeet__semilorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(563,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(1923,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(402,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(1597,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)],[402]) ).

thf(88,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(982,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)],[88]) ).

thf(99,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(1004,plain,
    ! [A: $i] :
      ( ( A @ class_HOL_Otimes )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(299,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(1399,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)],[299]) ).

thf(750,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(2270,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)],[750]) ).

thf(415,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(1621,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)],[415]) ).

thf(406,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(1606,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)],[406]) ).

thf(582,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(1962,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)],[582]) ).

thf(102,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(1009,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)],[102]) ).

thf(472,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(1737,plain,
    ! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(444,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(1681,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)],[444]) ).

thf(333,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(1463,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(615,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(2018,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)],[615]) ).

thf(527,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(1848,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)],[527]) ).

thf(308,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(1416,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)],[308]) ).

thf(662,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(2106,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(336,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(1468,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(132,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(1069,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(557,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(1912,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(705,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(2177,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)],[705]) ).

thf(781,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(2321,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(573,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(1944,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(284,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(1367,plain,
    ! [A: $i] :
      ( ( A @ class_Ring__and__Field_Osemiring__0 )
      | ~ ( A @ class_Power_Orecpower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(347,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(1490,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)],[347]) ).

thf(117,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(1037,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Olinorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(766,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

thf(2297,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(490,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(1769,plain,
    ! [A: $i] :
      ( ( A @ class_Orderings_Oord )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).

thf(1917,plain,
    ! [A: $i] :
      ( ( A @ class_LOrder_Olorder )
      | ~ ( A @ class_Wellfounded__Recursion_Owellorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(701,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(2170,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(142,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(1088,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)],[142]) ).

thf(105,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(1014,plain,
    ! [A: $i] :
      ( ( A @ class_OrderedGroup_Omonoid__mult )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(83,axiom,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(972,plain,
    tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(2522,plain,
    $false,
    inference(e,[status(thm)],[2199,2094,1024,1369,2295,1105,1729,846,1850,1982,941,1818,1554,2250,2163,892,1879,1337,2109,2131,1454,2072,1767,1179,2331,1956,1950,1549,1211,1882,2231,1522,2062,1443,1618,1401,2014,1205,1591,1142,1305,1437,1041,1750,977,1158,2309,1422,1939,2248,1793,1533,1173,1486,1608,1655,1756,2035,1735,2141,1919,945,2042,930,1458,1497,1705,1078,1426,1164,1999,2168,1260,1063,1954,1354,2146,1095,1746,1441,1613,1359,1386,2082,1475,1803,1127,1782,1391,1576,2020,841,973,1046,1650,1645,1921,2067,1967,2136,1904,1518,1703,1228,1482,1254,1628,1287,1709,1430,1871,1323,802,1826,1313,2185,1992,949,1055,1409,1760,1298,1330,1860,1264,1511,2274,917,1832,934,1191,1059,1132,1545,817,853,1379,1514,1147,2049,1319,1479,1013,1568,2158,1232,1347,1572,1741,881,2024,1641,2301,1494,2007,2237,924,1373,2259,1418,1828,1151,2034,1960,905,1946,1465,2324,2027,1811,1450,1109,1632,1136,834,1864,2122,1383,1020,2254,1581,2335,966,1183,1283,2058,1169,1377,2281,877,1886,1072,1201,2154,2205,1564,1526,2137,2002,998,1345,988,2286,2103,1405,1697,1242,2011,1691,793,1153,2118,810,2047,1067,1868,1057,1074,1604,1470,1915,1311,2232,2307,2061,2000,1636,1274,2264,1343,1021,1580,2147,1666,2132,1238,1560,1900,1723,910,957,1223,894,1123,862,1570,1676,2133,1502,820,1824,1619,2032,815,1365,1687,1624,2179,2313,1281,1634,1291,1910,1106,1032,1602,1968,879,1888,1296,1787,2181,1195,2211,1407,2300,1234,1762,1328,1375,1856,1672,1878,869,1118,2268,1397,2245,1350,874,2115,1270,1772,1111,1970,980,1498,1587,1540,1006,1138,1719,1683,884,1160,1361,1292,901,1424,1791,1028,1082,2023,1964,1942,1659,1739,1461,1414,2053,1842,2038,1446,1016,1207,2085,1039,970,2317,1744,837,997,1099,2304,1456,1266,2243,1932,984,1799,1984,1715,1979,2272,2140,1393,1525,2285,1114,1668,1974,1060,1050,1002,1852,2052,1599,1246,1333,792,1779,1695,921,2076,1035,1071,1187,1663,2189,888,926,1434,1857,1991,1318,1086,938,2208,805,2057,1846,1026,1895,1167,953,1185,794,2338,1996,1648,1727,1103,2149,1927,2121,2235,906,1278,1906,1754,2292,1301,1595,975,1615,843,1752,1929,2016,1388,875,1535,1403,1965,1520,1124,2225,1884,1795,1701,1256,1226,1488,936,2220,1371,1733,1997,1332,1092,919,1258,947,1638,1428,2161,2029,2326,1707,2293,2166,1090,2319,1356,2079,1209,831,2214,1048,1349,1144,1771,1122,1439,1175,2151,2229,1574,1011,2257,1589,1492,2299,1043,1801,2197,1307,2182,1080,1339,858,2111,1630,2267,1731,1862,848,1325,915,1556,2278,1820,890,1667,2180,2129,2343,799,1162,1149,964,943,1022,2252,1177,1381,2329,932,1952,1171,2075,1198,1699,1213,1643,883,2064,1113,1477,2101,1250,2303,2156,922,1805,1562,2212,959,2171,2051,1044,1445,1528,986,2288,1775,2244,1000,1076,1626,2239,1583,1809,2096,1873,1203,1467,795,1420,2124,1134,1472,1958,1551,2054,1948,1758,2107,812,1509,1990,2202,2333,1145,1018,968,1181,823,855,1516,872,1225,1647,2175,1780,1531,993,1547,1748,1611,1156,1566,2143,1941,1252,1230,1484,2160,1711,2092,1452,1869,1785,1262,2044,1130,1790,1987,1432,2165,2276,2219,2128,1830,1763,1538,951,808,1285,1738,1218,1934,2113,1981,1504,1008,1272,2266,2056,2247,1543,1766,1972,2320,1506,1585,1094,1140,1670,1797,1717,2030,1240,991,1617,2013,1839,2088,2045,1685,1553,2194,1412,1216,1126,1866,1807,1316,1084,1321,1834,1913,2310,1844,903,1448,2187,1189,2305,2342,1289,2226,1276,1326,2290,2135,1508,1481,1101,2004,2026,1854,961,1721,963,2273,2174,2283,1341,896,2098,1674,1639,1244,1822,995,1558,2152,2262,2009,1030,1689,1777,1294,1440,2066,1193,2183,1513,2120,2315,1994,2019,899,1661,1893,2036,1309,2123,2287,1774,1725,1578,1678,2155,1097,1395,1593,1876,1248,867,865,1116,1908,1303,1986,1989,1363,1816,1657,1197,2091,828,1065,2040,955,1610,1436,1859,1335,1693,2070,897,1410,2340,1165,886,1742,928,1352,1268,860,1537,2265,1976,908,1925,1713,1902,1120,1930,839,1236,2241,2127,1977,1129,1500,1923,1597,982,1004,1399,2270,1621,1606,1962,1009,1737,1681,1463,2018,1848,1416,2106,1468,1069,1912,2177,2321,1944,1367,1490,1037,2297,1769,1917,2170,1088,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07  % 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
% 0.12/0.37  % Computer : n004.cluster.edu
% 0.12/0.37  % Model    : x86_64 x86_64
% 0.12/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37  % Memory   : 8046.5625MB
% 0.12/0.37  % OS       : Linux 6.8.0-71-generic
% 0.12/0.37  % CPULimit : 300
% 0.12/0.37  % WCLimit  : 300
% 0.12/0.37  % DateTime : Sat Sep 26 08:18:52 UTC 2026
% 0.12/0.37  % CPUTime  : 
% 0.12/0.37  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
% 0.90/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.04/1.35  % [INFO] 	 Parsing done (395ms). 
% 2.04/1.36  % [INFO] 	 Running in sequential loop mode. 
% 3.04/1.76  % [INFO] 	 eprover registered as external prover. 
% 3.04/1.77  % [INFO] 	 Scanning for conjecture ... 
% 3.53/1.98  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ... 
% 4.70/2.29  % [INFO] 	 Axiom selection finished. Selected 787 axioms (removed 570 axioms). 
% 5.78/2.51  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.78/2.53  % [INFO] 	 Type checking passed. 
% 5.78/2.54  % [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 ... 
% 20.63/6.03  % External prover 'e' found a proof!
% 20.63/6.04  % [INFO] 	 Killing All external provers ... 
% 20.63/6.04  % Time passed: 5537ms (effective reasoning time: 4669ms)
% 20.63/6.05  % Axioms used in derivation (787): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Opordered__comm__semiring_14, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, 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, cls_List_Olistrel__Cons1_0, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, 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, 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, cls_Datatype__Universe_Ousum__In1I_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, 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, cls_List_Oappend__in__lists__conv__iff2_0, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsarity_nat_32, clsarity_nat_26, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Olength__remdups__eq__iff2_0, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, 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, cls_List_Olistrel__Cons2_1, cls_Divides_Omod__eq__0D__dest_0, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, clsarity_prod_0, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, cls_List_ONil__is__append__conv__iff2_0, clsrel_Power_Orecpower_14, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_OrderedGroup_Omonoid__mult_2, clsarity_IntDef__Oint_24, clsrel_OrderedGroup_Osemigroup__add_0, 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, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, 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, clsrel_Power_Orecpower_21, clsrel_Wellfounded__Recursion_Owellorder_4, clsrel_Power_Orecpower_6, clsarity_nat_10, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, cls_Wellfounded__Recursion_Owf__insert__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_IntDiv_Ozdvd__0__left__iff2_0, cls_Nat_Oless__Suc0__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, cls_Set_Osingleton__insert__inj__eq__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, cls_Datatype__Universe_OusumE_2, clsrel_Ring__and__Field_Osemiring_1, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Finite__Set_OFinites_OemptyI_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, clsrel_Ring__and__Field_Oordered__semidom_23, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, 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, cls_Datatype__Universe_Ousum__In0I_0, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsarity_nat_25, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsarity_IntDef__Oint_56, clsarity_sum_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsarity_set_2, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Wellfounded__Recursion_Owellorder_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_List_Olistrel__Nil1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, 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, cls_Set_OComplI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Ring__and__Field_Opordered__comm__semiring_8, cls_Relation_OconverseE_1, cls_Finite__Set_Ofinite__Int_0, cls_Nat_Oless__one__iff1_0, cls_Datatype__Universe_OdsumE_1, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, 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, 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_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, cls_List_ONil__is__append__conv__iff1_0, 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, clsarity_IntDef__Oint_38, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, clsrel_OrderedGroup_Oab__semigroup__mult_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, clsrel_Ring__and__Field_Opordered__semiring_2, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, clsrel_Wellfounded__Recursion_Owellorder_5, cls_Relation_Orel__compE_0, clsrel_Ring__and__Field_Osemiring__0_2, cls_SetInterval_OlessThan__iff__iff1_0, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Osemiring__0_7, cls_Set_OUnCI_1, clsarity_nat_36, clsarity_nat_18, cls_Set_OinsertCI_0, 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, cls_List_Oset__empty__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_16, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, clsrel_Ring__and__Field_Oordered__semidom_13, cls_Product__Type_OPair__eq__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, cls_Set_OPow__iff__iff2_0, cls_Finite__Set_Ofinite__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, cls_List_Olength__remdups__leq_0, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Power_Orecpower_13, clsrel_Ring__and__Field_Oordered__semidom_24, clsrel_Power_Orecpower_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, 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, cls_List_Oappend__in__lists__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_35, clsrel_Ring__and__Field_Oordered__semiring__strict_21, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, 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, cls_Datatype__Universe_OdprodE_1, clsarity_nat_44, clsrel_Ring__and__Field_Ocomm__semiring_2, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, clsrel_Ring__and__Field_Osemiring__1__cancel_4, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_3, cls_List_OlistsE_0, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Osemiring__1_3, cls_Finite__Set_Ofinite__Un__iff1_0, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, cls_Set_OUNIV__I_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, cls_Set_OCompl__eq__Compl__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, 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_Ocomm__semiring_5, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Opordered__semiring_7, clsarity_IntDef__Oint_64, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, cls_Set_OUnE_0, clsrel_Ring__and__Field_Oordered__semiring__strict_11, cls_List_Owf__lex_0, cls_SetInterval_OatMost__eq__iff__iff1_0, cls_List_Olistrel__Cons2_0, clsarity_nat_27, cls_Relation_ODomainI_0, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, cls_Set_OinsertE_0, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_OrderedGroup_Ocomm__monoid__add_1, 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, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, 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, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, clsarity_nat_38, clsrel_Ring__and__Field_Osemiring__1__cancel_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, clsrel_Wellfounded__Recursion_Owellorder_3, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Ocomm__semiring__1_11, cls_Datatype__Universe_OusumE_1, 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, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_IntDef__Oint_20, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_GCD_Ogcd__dvd1_0, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, clsarity_set_3, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, cls_SetInterval_OatMost__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, cls_SetInterval_Ofinite__atLeastLessThan_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, cls_Set_OUn__empty__iff1_0, clsrel_Power_Orecpower_10, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, clsrel_Ring__and__Field_Opordered__cancel__semiring_2, cls_Wellfounded__Recursion_Owf__insert__iff2_0, clsrel_Ring__and__Field_Osemiring__0_6, cls_Set_Oempty__subsetI_0, clsrel_Ring__and__Field_Oordered__semidom_17, cls_Relation_OIdI_0, clsarity_IntDef__Oint_26, clsrel_Ring__and__Field_Osemiring__1_0, clsarity_IntDef__Oint_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, cls_List_Oappend__is__Nil__conv__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, 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_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_Ring__and__Field_Opordered__cancel__comm__semiring_2, clsarity_nat_37, cls_Nat_Oadd__gr__0__iff2_1, 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_LOrder_Olorder_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, 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_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, cls_List_Osame__append__eq__iff1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, cls_SetInterval_OatLeast__iff__iff2_0, clsarity_IntDef__Oint_37, cls_GCD_Ogcd__greatest__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, cls_Datatype_Oelem__o2s__iff1_0, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__0_10, cls_Relation_OconverseE_0, clsarity_IntDef__Oint_42, cls_IntDiv_Ozdvd__1__left_0, cls_List_Olength__greater__0__conv__iff2_0, 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, cls_Datatype__Universe_OdsumE_2, 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, clsrel_LOrder_Omeet__semilorder_0, cls_List_Olist_Oinject__iff1_1, clsrel_Power_Orecpower_3, 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cls_GCD_Ogcd__greatest__iff__iff1_1, clsrel_Orderings_Olinorder_2, cls_Datatype__Universe_OuprodE_0, clsarity_nat_45, cls_Set_ODiffE_0, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_12, 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__semiring__1__cancel_4, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Relation_ORangeI_0, cls_Divides_Odvd__triv__right_0, cls_List_Oset__empty__iff1_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, 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_Oordered__semidom_4, cls_Nat_Onot__add__less1__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4, clsarity_nat_28, clsrel_Ring__and__Field_Osemiring__0__cancel_6, clsarity_IntDef__Oint_40, 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_6, cls_Set_OIntI_0, 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, clsarity_nat_23, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, 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clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsarity_IntDef__Oint_61, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Osemiring__0_3, cls_List_Owf__lenlex_0, clsarity_IntDef__Oint_12, clsarity_fun_0, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Opordered__comm__semiring_7, clsrel_Ring__and__Field_Oordered__semidom_14, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, clsarity_nat_30, cls_Relation_Orel__compE_1, clsarity_set_4, clsarity_nat_41, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, clsrel_Ring__and__Field_Osemiring__0__cancel_0, cls_List_Olength__remdups__eq__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, cls_Set_OinsertCI_1, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Power_Orecpower_19, cls_List_Oappend__self__conv__iff1_0, 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_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6
% 21.86/6.05  % No. of inferences in proof: 1583
% 21.86/6.06  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5537 ms resp. 4669 ms w/o parsing
% 23.81/6.49  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.31/6.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------